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Results tagged with arithmetic-geometry
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user 4008
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
13
votes
Simplest example of jumping of cohomology of structure sheaf in smooth families?
One example is given by Enriques surfaces in characteristic $2$. There are three types depending on the value of $\mathrm{Pic}^\tau$ (as a group scheme) which can be either $\mathbb Z/2$, $\mu_2$ or $ …
- 22.6k
9
votes
Simplest example of jumping of cohomology of structure sheaf in smooth families?
This is an attempt to realise Sándor's program of getting an example based on
Kodaira vanishing or non-vanishing varying in a family. It will be done by
keeping the surface fixed but varying the line …
- 22.6k
6
votes
Have people successfully worked with the full ring of differential operators in characterist...
Certainly the fact that the ring of differential operators is non-Noetherian is an inconvenience but it is not clear if it is more than that. For instance one can define the notion of holonomic module …
- 22.6k
4
votes
Is it possible to classify all Weil cohomologies?
If we believe in the standard conjectures (or something similar) so that the category of motives is Tannakian, then a Weil cohomology theory is just a fibre functor and as such twists of each other (t …
- 22.6k