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Results tagged with ag.algebraic-geometry
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user 14672
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
9
votes
Accepted
Frobenius splitting and derived Cartier isomorphism
Keeping the notation of the question $X$ is a smooth variety over an algebraically closed field $k$ of characteristic $p>\dim X$. Just following along from Decomposition of the de Rham Complex by V Sr …
- 970
17
votes
2
answers
1k
views
Formal Schemes Mittag Leffler
Here is a question that I'm just copying from Math Stack Exchange that I asked awhile ago. It has just been sitting there unanswered, and although I haven't really thought about it since I posted it, …
- 970
15
votes
1
answer
1k
views
Lifting to Characteristic 0 not over W
I thought of this several months ago and forgot about it. Now I rethought of it again and I just can't find it anywhere in the literature, so I'll ask here.
Is it known whether or not there exists a …
- 970
2
votes
What should be taught in a 1st course on Riemann Surfaces?
Although it is sort of indirectly related, it might be nice to talk about some introductory abelian variety things (as in the first few pages of Mumford's Abelian Varieties). The motivation would come …
- 970
11
votes
3
answers
2k
views
What is the difference between Grothendieck groups K_0(X) vs K^0(X) on schemes?
More specifically, I was wondering if there are well-known conditions to put on $X$ in order to make $K_0(X)\simeq K^0(X)$. Wikipedia says they are the same if $X$ is smooth. It seems to me that you g …
- 970
20
votes
3
answers
6k
views
Closed vs Rational Points on Schemes
Background: When Ueno builds the fully faithful functor from Var/k to Sch/k he mentions that the variety $V$ can be identified with the rational points of $t(V)$ over $k$. I know how to prove this on …
- 970
10
votes
1
answer
1k
views
$\ell$-adic Weil cohomology theory
I have a reference or counterexample request. Suppose $k$ is a field and $\ell\neq char(k)$. There are several common references that show that $H^i_{et}(-, \mathbb{Q}_\ell )$ is a Weil cohomology the …
- 970