James Davidoff

369 reputation

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visits	member for	2 years, 6 months
	seen	Oct 10 '12 at 1:53
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	369 reputation	bio	website		visits	member for	2 years, 6 months
16 badges		location			seen	Oct 10 '12 at 1:53

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Dec 2	revised	Cohomology of $\mathcal O_X$ for toric varieties whoops
Dec 2	asked	Cohomology of $\mathcal O_X$ for toric varieties
Dec 2	comment	Cohomological decomposition of tensor sheaves? Oh wow, I thought $H^m(X, \mathcal O_X)=0$ for all $m>0$!!
Dec 2	accepted	Cohomological decomposition of tensor sheaves?
Dec 2	comment	Cohomological decomposition of tensor sheaves? Why is it false for $\mathcal O_X$? The only non-vanishing cohomology is $H^0(X,\mathcal O_X)$, so doesn't the formula hold?
Dec 2	asked	Cohomological decomposition of tensor sheaves?
Nov 30	accepted	Is a regular sequence ordered?
Nov 29	asked	Is a regular sequence ordered?
Nov 17	accepted	Quotient spaces and equivariant cohomology
Nov 15	awarded	Teacher
Nov 15	answered	Negation of if and only if?
Nov 15	comment	Quotient spaces and equivariant cohomology I'm not very familiar with stacks, or with the details of GIT if $G$ is not a torus, but at least when it is the torus the GIT procedure removes the non-free points from $Y$ before quotienting. $X//G$ is supposed to give a scheme $Y$, and I assume that it is constructed thus to avoid having the quotient be a stack.
Nov 15	revised	Quotient spaces and equivariant cohomology Clarified
Nov 15	asked	Quotient spaces and equivariant cohomology
Nov 12	asked	Yoga of localization in categories?
Nov 6	awarded	Supporter
Nov 6	accepted	Why is stable equivalence necessary in topological K-theory?
Nov 5	comment	Why is stable equivalence necessary in topological K-theory? I think there's something basic I'm missing. Stable equivalence is an equivalence relation on isomorphism classes of bundles. Say $E$ and $F$ are isomorphism classes. Then it appears to me that $E = F$ iff $E + G = F + G$ in K-theory. I suppose my question is, why is stable equivalence not "lies in the same isomorphism class"? In particular, what is an example of two non-isomorphic bundles such that when a trivial bundle is added to them, they become isomorphic?
Nov 4	comment	Why is stable equivalence necessary in topological K-theory? Hi Ryan, thanks for your clarification, but it's still murky for me. I don't see why $E \cong F \not \Leftrightarrow (E \oplus G) \cong (F \oplus G)$
Nov 3	comment	Why is stable equivalence necessary in topological K-theory? Are you saying that stable equivalence endows isomorphism classes with a formal inverse? That I don't see.