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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
9
votes
How do non-trivial global differentials give non-trivial cohomology classes in positive char...
Although Felipe answered your question, let me come back to David's wish, and give an answer using and advocating crystalline cohomology:
First, if $X$ is, say, smooth and proper over a field $k$, t …
8
votes
Accepted
Hodge spectral sequence for algebraic stacks
Did you have a look at Satriano's article de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities?
5
votes
Simplest example of jumping of cohomology of structure sheaf in smooth families?
By the way, for Enriques this more than just an example - it reflects their classification: the moduli space of Enriques surfaces is connected in any characteristic. All such surfaces arise as desingu …