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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes
0 answers
468 views

Comparison between singular and etale cohomology in Batyrev's paper on Birational Calabi-Yau...

My question refers to the paper http://arxiv.org/pdf/alg-geom/9710020.pdf where Batyrev proves that birational Calabi-Yau algebraic varieties have equal Betti numbers by counting points over finite fi …
Tom Lovering's user avatar
6 votes
1 answer
544 views

Class field theory using only ideles of norm 1

I am a total non-expert, so the answer to this question may be obvious, but here goes. In Chevalley's formulation of CFT we get Artin maps $J_k \rightarrow Gal(L/k)$, where $J_k$ is the group of all …
Tom Lovering's user avatar
4 votes
1 answer
286 views

Regular singularities and the infinitesimal site

Suppose I have a smooth non-proper algebraic variety $X/\mathbb{C}$. A vector bundle with flat connection (``differential equation'') on $X$ extends, as was noted by Grothendieck, to a coherent crys …
Tom Lovering's user avatar
9 votes
1 answer
2k views

Torsors and the fpqc topology

Fix a scheme $S$, a group scheme $G/S$ (let us say smooth, maybe even affine with some finiteness conditions if you like), and suppose I have some other $S$-scheme $P$ with a right $G$-action. We want …
Tom Lovering's user avatar