tea.mathoverflow.net - Discussion Feed (The ideal D_k.)

Yemon Choi comments on "The ideal D_k." (10050)

Yemon Choi — Sun, 31 Oct 2010 21:13:13 -0700

Just caught up with this thread, so +1 to Scott.

Harry Gindi comments on "The ideal D_k." (10020)

Harry Gindi — Sun, 31 Oct 2010 02:03:48 -0700

Whatever you say, boss!

Scott Carnahan comments on "The ideal D_k." (10018)

Scott Carnahan — Sun, 31 Oct 2010 00:58:11 -0700

I don't think such a question is appropriate for MathOverflow, and asking such a question is a sort of social error when it comes from someone who should know better. When you ask a question on this site, we expect that you have already put in some time trying to find an answer by other avenues, since in the act of posting, you are going to take time out of a lot of other people's busy lives. In this case, the readers aren't being rewarded with any interesting information (e.g., the situation would be different if you had found some unfamiliar notation in an old paper). I would have voted to close if I were awake and present. I don't think extenuating circumstances like a lost phone or reluctance to email the instructor make much of a difference here.

Harry Gindi comments on "The ideal D_k." (10014)

Harry Gindi — Sat, 30 Oct 2010 20:37:03 -0700

Dear Shevek,

For the purpose of full disclosure, I note that earlier today I had lost my cellular telephone (and did not get it back until a few hours ago) and was under the impression that I would not be able to get a quick response by e-mailing the instructor (although I found out later that this was not in fact the case). I hope that these extenuating circumstances are sufficient to slake your wrath.

Shevek comments on "The ideal D_k." (10013)

Shevek — Sat, 30 Oct 2010 20:26:22 -0700

Yes of course, Harry. But your dismissal of my comment as a red herring without actually addressing the meat of the comment at all is itself misguided and rude.

Given that neither one of us wants noise on MO, can you justify or explain in what sense your question is _not_ noise?

For your amusement you might like to consider the following two situations:

A) My question could be answered in a flash by asking my classmate, but instead I will ask MathOverflow.

B) My question could be answered in a flash by asking google, but instead I will ask MathOverflow.

and meditate on their difference.

p.s. It is not my intention to be abrasive or rude.

p.p.s. I agree that just because a question is about notation doesn't make it bad.

Harry Gindi comments on "The ideal D_k." (10012)

Harry Gindi — Sat, 30 Oct 2010 19:48:52 -0700

@Shevek: It's your right to have that opinion, but your comment was a red herring in the passive, not active sense as follows:

(idiomatic) A clue that is misleading or that has been falsified, intended to divert attention.

That is, I was not claiming that you were intending to deceive or divert attention, merely that your conflation of the D_4 example and the D_k example was misleading.

Regarding "noise" that you would rather not have on MO, I would prefer not to have questions like this one, but it has (as of now) no votes to close. It is also certainly much closer to a question that belongs on Math.SE than my question.

Here's my point: Just because a question is about notation doesn't make it bad.

Shevek comments on "The ideal D_k." (10011)

Shevek — Sat, 30 Oct 2010 19:38:41 -0700

@Harry: No, my comment is not a red herring, and your comment about my comment is narrow-sighted. What you can rightly conclude is that my conflation of the examples of D_4 and D_K is not great. But was that the most important part or point of my comment? No it was not. I have a perfectly legitimate opinion about your question, as do others.

Harry Gindi comments on "The ideal D_k." (10009)

Harry Gindi — Sat, 30 Oct 2010 18:11:14 -0700

@wilton: I like to think that I've mellowed out in my old age.

HJRW comments on "The ideal D_k." (10008)

HJRW — Sat, 30 Oct 2010 17:57:26 -0700

I ask: Was it really necessary to respond so harshly?

Harry, I'm struggling to think of an occasion when the tone of your comments was dictated by necessity.

Harry Gindi comments on "The ideal D_k." (10007)

Harry Gindi — Sat, 30 Oct 2010 17:17:15 -0700

@Pete L. Clark:

You always seem to assume I have the worst intentions. There is a good faith question on policy here, and I am raising it. If anything, your accusation that I'm trolling far more likely fits the definition of "trolling". I urge you to reconsider your comment.

@Shevek:

Your comment is a red herring. Here's why (google searches by notation and general notion):

Google search for "D_4 Group"

link

Which results in the correct answer being found immediately!

Now search for the different by notation.

Google search for "D_k ideal"

link

Google search for "D_k ideal primes ramification"

link

I knew that the ideal in question was not the discriminant, and that's the only thing that comes up in those searches. In fact, after a few pages of the above searches, it's still not clear to me that the different will come up after a reasonable number of them.

Shevek comments on "The ideal D_k." (10006)

Shevek — Sat, 30 Oct 2010 17:09:00 -0700

Hi Harry. I definitely agree that it can hard to look up the meaning of symbol. But nevertheless I don't think that your question needed to be asked on MathOverflow. Why? Well, you could have just asked one of your fellow students and you would have had your question answered immediately, whereas any question posted on MO will take maybe 1 minute of time away from a hundred or so busy people. If this were some random symbol that you had come across and had no way of figuring out what it was referring to, then sure your argument might work, but you came across this symbol with full context of where it came from (you simply didn't write down the definition in class!), so you were fully aware of obvious places where to find out the symbol from: namely, all the other people who where in the class! I definitely wouldn't want people coming on MO asking "I forgot to write down the definition of D_4 in group theory class today, what is it?" which is a pretty similar situation. Sure, someone _could_ just answer "dihedral group", but it is noise that I would prefer MO not to have, and surely it goes against MO policy. The notion of a different is a similarly basic concept taught in any introductory course on algebraic number theory.

Pete L. Clark comments on "The ideal D_k." (10005)

Pete L. Clark — Sat, 30 Oct 2010 17:06:04 -0700

I regard Harry's behavior here as simple trolling, and I encourage others to simply ignore it. There is no good faith question or policy issue here.

Emerton comments on "The ideal D_k." (10004)

Emerton — Sat, 30 Oct 2010 16:43:40 -0700

Dear Harry,

I subscribe to the theory that you can address a correspondent by the name they sign their correspondence with, and I'm happy for others to apply this theory to me! So calling me Matthew or Matt is fine.

Regards,

Matthew

P.S. The best thing to come out of this is Franz Lemmermeyer's joke.

Harry Gindi comments on "The ideal D_k." (10002)

Harry Gindi — Sat, 30 Oct 2010 15:55:08 -0700

@voloch: I read the MO FAQ, and at least as far as I can tell, my question was alright to ask. Maybe one of the moderators can make a ruling on this.

Here is the relevant part of the MO FAQ (since at least my question doesn't fall into one of the expressly prohibited categories):

MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books. Of course, individual questions don't have to be worthy of an article, and they don't have to be about new mathematics. A typical example is, "Can this hypothesis in that theorem be relaxed in this way?"

And by the way, I am not asking for people to give me special treatment. On the contrary, I really believe my question lies within what is admissible for at least one reasonable interpretation of the FAQ (and hence I would like to know Anton or Scott's opinion).

voloch comments on "The ideal D_k." (10001)

voloch — Sat, 30 Oct 2010 15:51:37 -0700

Harry: "I don't see how it is against MO policy to ask this sort of question" It's not of interest to research mathematicians. It's definitely against MO policy. You are complaining with a sense of entitlement as if your high MO rep gave you leeway to ask such questions. On the contrary, you should know better. If this kind of question is allowed of you, it should be allowed of others and where is it going to end? You were treated harshly precisely because people expected more of you.

Harry Gindi comments on "The ideal D_k." (10000)

Harry Gindi — Sat, 30 Oct 2010 15:45:12 -0700

@Noah: Regarding sending it to math.SE, the question was so easy and would not have taken any amount of time to answer, for any sort of expert or person knowledgeable in the subject area. If I had posted it on math.SE, which experts don't check nearly as often, it would have taken substantially longer to get an answer. Since it was not a homework problem I don't see how it is against MO policy to ask this sort of question. It may not really be of interest to research mathematicians, but it is certainly a question that could be relevant to someone reading a paper with unexplained notation, and reading the MO FAQ, this seems to be admissible.

Noah Snyder comments on "The ideal D_k." (9999)

Noah Snyder — Sat, 30 Oct 2010 15:37:37 -0700

As for the actual question, a good first place to look if you want textbook info on something related to number theory but only have access to the internet and not a book is J.S. Milne's page of notes: http://www.jmilne.org/math/

Noah Snyder comments on "The ideal D_k." (9998)

Noah Snyder — Sat, 30 Oct 2010 15:35:55 -0700

Close and refer to math.SE is the right response here, right?

voloch comments on "The ideal D_k." (9997)

voloch — Sat, 30 Oct 2010 15:34:53 -0700

Problem 20 on Chapter 7 of your textbook. Get the book, it's really good.

Harry Gindi comments on "The ideal D_k." (9996)

Harry Gindi — Sat, 30 Oct 2010 15:10:57 -0700

@Qiaochu: Thanks for doing that. I appreciate it.

Hailong Dao comments on "The ideal D_k." (9995)

Hailong Dao — Sat, 30 Oct 2010 15:03:46 -0700

Harry, thanks. Now that I see it, I can also see why some people might have reacted strongly to your question. It sounded like you could have just asked your classmate/instructor.

Qiaochu Yuan comments on "The ideal D_k." (9994)

Qiaochu Yuan — Sat, 30 Oct 2010 15:03:37 -0700

Ah, found it; I was looking in the wrong deleted posts menu.

A question for which I must apologize before asking:

I failed to write down the definition of the ideal "Dk" of the ring of algebraic integers of a number field k when I was in class earlier this week, and I forgot both what it is called and its definition.

I think it's the ideal measuring the ramification of a prime, but I'm not sure.

An answer to this question may just be one word (the name of the ideal). I will have no trouble looking it up once I know the name.

Again, sorry.

The negative votes are pointless. There's no way for me to look this up, so give it a rest. – Harry Gindi 4 hours ago

Did someone hijack Harry's account? – Franz Lemmermeyer 4 hours ago

No. I don't see why this is such a problem. – Harry Gindi 4 hours ago

Do you not have enough reputation IRL to ask your professor or a classmate? – Erik Davis 4 hours ago

The notation appears on my homework, and I don't remember what it is. It's not like I'm asking you to solve the problem... – Harry Gindi 4 hours ago

Can't you ask the instructor or one of your fellow students? Why pollute MO? Googling "ramification in number fields" is sure to give you the answer. – Felipe Voloch 4 hours ago

@Erik: If it's so easy, just answer it. It's 1PM on a saturday. I can't find my cell phone, and my professor probably won't answer my e-mail until tomorrow night. – Harry Gindi 4 hours ago

In that case, it's different. – Franz Lemmermeyer 4 hours ago

Erik Davis was out of line. Emerton makes good points, but I have to agree with Harry that it is incredibly hard to look up the definition of a notation you don't know the name of, especially given that different authors use different notation and don't always have a list of all of their notation. For example, Neukirch doesn't have such a list, and his notation for the different is a capital fraktur D, which is different (ha!) from both of the two notations Harry has described.

Maybe an acceptable compromise is to agree that such questions should be asked on math.SE in the future.

Harry Gindi comments on "The ideal D_k." (9993)

Harry Gindi — Sat, 30 Oct 2010 14:54:28 -0700

@Hailong: It was almost exactly this:

I apologize in advance for asking this question.

I forgot to copy down the definition of the notation $\mathcal{D}_k$ of the ring of integers of a number field. I remember it has something to do with tracking the ramification of primes.

An answer to this question can be as short as a single word, since I have no problem looking it up once I know the name. Sorry again!

Hailong Dao comments on "The ideal D_k." (9992)

Hailong Dao — Sat, 30 Oct 2010 14:44:17 -0700

Harry: ah right, I forgot that even the OP can't see the question he/she deleted! My apology, but I am still curious what your question was.

Harry Gindi comments on "The ideal D_k." (9991)

Harry Gindi — Sat, 30 Oct 2010 14:40:43 -0700

If someone with proper privileges could be so kind as to copy and paste the thread, I would appreciate it.

@Hailong: I believe that this is the Dedekind different, and the other ones are generalizations to more general cases where the dedekind different can fail to be well-behaved. It seems that the number-theoretic version (i.e. the Dedekind different) makes sense over any Dedekind ring, but probably no further.

Hailong Dao comments on "The ideal D_k." (9990)

Hailong Dao — Sat, 30 Oct 2010 14:39:18 -0700

Dear Harry: it is a little strange that you want to debate something most people can't see (I totally missed it, and I am kind of curious as I have seen a number of phrases like "Noetherian different", "Dedekind different" or even "homological different", but never learned them properly. Perhaps they are different from what you asked (-: ?)

Harry Gindi comments on "The ideal D_k." (9989)

Harry Gindi — Sat, 30 Oct 2010 14:32:04 -0700

Dear Emerton,

That's fair, but it's not exactly obvious where to look unless you already know where to look. It is hard to find the definition of a symbol if you're not already familiar with its name. Further, the different is often denoted $\mathfrak{d}_k$, in fraktur, not in calligraphy or script, so even looking in the index of notation (of a book, since most lecture notes do not have this feature) would not have been as easy as you're making it sound. Regarding the sheer number of books, sometimes that is unhelpful, since it makes it a monumental task when there are a variety of notations, or worse, when the concept is not covered in every one of those books.

Regards,

Harry

P.S. (Would you prefer that I address you as Professor Emerton, Emerton, Matthew, Matthew Emerton, Matt, Matt Emerton, etc? I usually go by the name in the meta post, but since you're signing your first name, I'd just like to know what you feel most comfortable with.)

Emerton comments on "The ideal D_k." (9988)

Emerton — Sat, 30 Oct 2010 14:29:27 -0700

Dear Harry,

There is no algebraic number theory in Serre's book. There are hundreds of algebraic number theory texts, all of which will be in your library. And there are dozens, if not hundreds, of sets of online notes on the subject too.

Regards,

Matthew

Harry Gindi comments on "The ideal D_k." (9987)

Harry Gindi — Sat, 30 Oct 2010 14:27:33 -0700

Dear Emerton,

It was a notation question, not a homework question (as there was no explicit or implicit request to answer a homework problem). Regarding books, I looked in Serre's book A Course in Arithmetic, and it's not in there, and I also searched Google and wikipedia for things like "ramification primes D_k" and turned up nothing.

Emerton comments on "The ideal D_k." (9986)

Emerton — Sat, 30 Oct 2010 14:22:23 -0700

Dear Qiaochu,

You will find it under tools/links/recently_deleted_posts .

Dear Harry,

As Voloch wrote, why didn't you just look in your (or any) textbook? Or just google "algebraic number theory .pdf" and read any of the hundreds of sets of lecture notes on algebraic number theory that will surely turn up on such a search? Or post on Math.SE?

I don't think that anyone reacted differently to how you react to calculus or linear algebra questions. Why do you think that your homework-related question should have been treated differently?

Regards,

Matthew

voloch comments on "The ideal D_k." (9984)

voloch — Sat, 30 Oct 2010 12:04:15 -0700

It could have been the different or could have been the discriminant, the subtle difference might have thrown off the homework problem (clearly it was one or the other). I downvoted and also voted to close. There was no excuse to first ask the instructor or a student or look in the textbook.

Qiaochu Yuan comments on "The ideal D_k." (9983)

Qiaochu Yuan — Sat, 30 Oct 2010 12:02:25 -0700

I can't find the question, so I don't have full information about this, but it seems unfortunate. Can you quote the question and comments?

Harry Gindi comments on "The ideal D_k." (9979)

Harry Gindi — Sat, 30 Oct 2010 10:56:15 -0700

I asked a question (now deleted) about the ideal D_k, where I was just looking for the name of the ideal (with proper context provided, of course). It could have just been answered and everyone could have gone on his or her merry way.

Unfortunately, I was lambasted and told to look on google. Fortunately for me, a colleague of mine e-mailed me and informed me that I was looking for the different. I spent a half hour looking before on google, and I was unable to find it (to answer those comments suggesting I do so).

It was a question with a definite answer that couldn't be found easily through a search engine or in a textbook. As a notation question, it was a question of dubious interest to mathematicians, but this was the only place I could think of to ask it and receive a quick answer to a quick question.

I ask: Was it really necessary to respond so harshly?