Comments for Stacks Project Blog
http://math.columbia.edu/~dejong/wordpress
Algebraic stacks and open source algebraic geometrySun, 30 Oct 2016 17:26:49 +0000hourly1https://wordpress.org/?v=4.7.2Comment on Challenge Accepted by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4149&cpage=1#comment-1136702
Sun, 30 Oct 2016 17:26:49 +0000http://math.columbia.edu/~dejong/wordpress/?p=4149#comment-1136702So why doesn’t that work?
]]>Comment on Completeness by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4123&cpage=1#comment-1136324
Sun, 03 Apr 2016 11:01:37 +0000http://math.columbia.edu/~dejong/wordpress/?p=4123#comment-1136324Was this post and April 1 joke? No textbook is complete. In my opinion, no textbook should be “complete”, at least, not if it is going to be used by students to learn a subject for the first time. Once I tried teaching an intro grad course out of a textbook that was written more as an encyclopedia than a textbook. Before each lecture, I spent hours tracing forward through the book trying to determine which baroque lemmas would be used later and which would not. That was not the author’s fault: it was my fault for trying to teach out of a book that was not suitable for classroom use.
]]>Comment on Blowing down exceptional curves by Johan
http://math.columbia.edu/~dejong/wordpress/?p=4115&cpage=1#comment-1136227
Mon, 07 Mar 2016 11:51:45 +0000http://math.columbia.edu/~dejong/wordpress/?p=4115#comment-1136227Sorry, I forgot to say that E is an effective Cartier divisor; I have edited the post. The fact that E is an effective Cartier divisor implies that every local ring of X at a closed point of E is regular of dimension 2. But part of the problem with not assuming more about X is that it need not be the case that X has dimension 2 in an open neighbourhood of E, although I have no counter example.
]]>Comment on Blowing down exceptional curves by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4115&cpage=1#comment-1136224
Mon, 07 Mar 2016 09:38:45 +0000http://math.columbia.edu/~dejong/wordpress/?p=4115#comment-1136224Just so I understand, is the ambient scheme regular of dimension 2, and does it contain $E$ as a Cartier divisor?
]]>Comment on Canonical divisor by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4093&cpage=1#comment-1136187
Thu, 18 Feb 2016 21:23:31 +0000http://math.columbia.edu/~dejong/wordpress/?p=4093#comment-1136187Maybe I am remembering the problem of constructing the relative Todd class as an element in K-theory for perfect morphisms (although presumably that is in SGA 6 . . .). Apart from the Q-coefficients issue (which seems unavoidable), Grothendieck’s formulation (for perfect morphisms, etc.) takes values in a ring formed from K-theory, which could be much bigger than the corresponding Chow groups (which Fulton defines in terms of the associated reduced scheme, so definitely lose information).
]]>Comment on Canonical divisor by Johan
http://math.columbia.edu/~dejong/wordpress/?p=4093&cpage=1#comment-1136186
Thu, 18 Feb 2016 12:28:54 +0000http://math.columbia.edu/~dejong/wordpress/?p=4093#comment-1136186In his book in section 18.3 he defines it for all schemes locally of finite type and separated and he defines the todd class of X in that generality too. Of course he uses Q coefficients and maybe what you are thinking about is whether you can do it with Z coefficients.
]]>Comment on Canonical divisor by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4093&cpage=1#comment-1136185
Thu, 18 Feb 2016 10:08:28 +0000http://math.columbia.edu/~dejong/wordpress/?p=4093#comment-1136185I do not agree that Fulton defines the Todd class of $X$ in “complete” generality. The Todd class homomorphism is defined in quite general circumstances. However, the question of whether the Todd class is defined for all separated, integral, finite type schemes is open, if memory serves. It is very related to the question of whether every such scheme admits an immersion to a smooth scheme. It is also related to the resolution property on the scheme. I believe that Totaro has an article exploring these connections.
]]>Comment on Canonical divisor by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4093&cpage=1#comment-1136182
Wed, 17 Feb 2016 09:42:41 +0000http://math.columbia.edu/~dejong/wordpress/?p=4093#comment-1136182I think the time mark of comments is on Dutch time (where I am it is 4:40 am, not 9:40 am).
]]>Comment on Canonical divisor by Jason Starr
http://math.columbia.edu/~dejong/wordpress/?p=4093&cpage=1#comment-1136181
Wed, 17 Feb 2016 09:40:38 +0000http://math.columbia.edu/~dejong/wordpress/?p=4093#comment-1136181That is not a canonical divisor; it is a canonical divisor class ðŸ™‚
]]>Comment on 5000 Pages by Stacks Project Party | Not Even Wrong
http://math.columbia.edu/~dejong/wordpress/?p=4079&cpage=1#comment-1136085
Sun, 07 Feb 2016 19:42:47 +0000http://math.columbia.edu/~dejong/wordpress/?p=4079#comment-1136085[…] event of the Manhattan social season, a party celebrating the fact that the Stacks Project has reached the milestone of 5000 pages. As far as anyone knows, no one has ever printed out the whole thing, but to give an idea of scale, […]
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