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Olivier's user avatar
Olivier's user avatar
Olivier
  • Member for 15 years
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What are the prime ideals of k[[x,y]]?
It is a regular local ring, hence UFD by Auslander and Buchsbaum. Am I missing something here?
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Published results: when to take them for granted?
@Pete: I have clarified my position with an edit. Apologies for the ambiguous statements.
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Published results: when to take them for granted?
Clarified my position upon the subject.
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Published results: when to take them for granted?
Took into account Milne's correction
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Published results: when to take them for granted?
Making a mistake in a list about notorious mistakes! Ah, the irony! Thanks a lot for the correction.
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Examples of common false beliefs in mathematics
I once made this very mistake, and it invalidates one of the main theorems of a published article I once quoted. A good reason in my opinion to specify what are the arrows when writing a sequence or a diagram: they are usually what you think they are, but hey, let's check.
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Books about history of recent mathematics
Or to put it in the form of the famous joke: a famous retiring algebraic topologist ends her retiring speech saying "Now that I am 65 and retiring, I want to spend my free time doing history". "And a good thing too", a historian in the room says "because now that I am 65 and retiring, I want to spend my free time doing algebraic topology".
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Books about history of recent mathematics
To write the history of a subject, one should better know how to do good history beforehand. Precious few people master both the technical historical knowledge and the technical mathematical knowledge required to write good recent mathematical history. For this reason, many (but not all) books mentioned in answers might be excellent books, but I wouldn't characterize them as historical, in the sense that they wouldn't (and by far) pass the standard requirement for a scholarly publication in the field of history.
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Examples of common false beliefs in mathematics
I think I kind of believed that until today.
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What are some examples of colorful language in serious mathematics papers?
@Kevin Buzzard: They are in print, in the same lecture mentioned by dke.
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Are there analogues of Beilinson's conjectures for motives with coefficients?
The quick answer is: yes there is, conjecturally everything carries over. See papers by K.Kato, D.Burns and M.Flach, T.Fukaya and K.Kato...
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Roadmap for studying arithmetic geometry
And the introduction states straight away that Deligne intends to publish a second article on the subject. The delay seems to be part of the never ending turmoil concerninh SGA 4,5 and 5.
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What are the maximal subgroups of GSp(2g,l)?
Just a historical comment: the classification of maximal subgroups of GL(2) for any finite field (not only Z/pZ) is due to Dickson so precedes Serre's paper by a good 70 years.
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weight 4 eigenforms with rational coefficients---is it reasonable to expect they all come from Calabi-Yaus?
@Emerton and Kevin Buzzard. Credit where credit its due: the fact that Serre's conjecture implies modularity of the H^3 of the Calabi-Yau is already in Serre's article for Manin (where the conjecture is formulated). This is theorem Théorème 6 unless I'm missing something.
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