4
votes
0answers
94 views

Complexes of arithmetic $\mathcal{D}$-modules with Frobenius structure

This is a question about the category $F\text{-}D^b_\mathrm{coh}(\mathscr{D}^\dagger_{\mathscr{X},\mathbb{Q}})$ of complexes of arithmetic $\mathscr{D}$-modules with Frobenius structure on a smooth ...
17
votes
1answer
2k views

Field with one element example?

$$\frac{1}{\mu(B)}\int_B \vert x \vert d\mu(x) = \frac{1}{p+1}$$ This formula holds for the unit ball in $\mathbb{Q_p}$. This formula also holds for $\mathbb{R}$ when $p=1$. Should one expect ...
7
votes
1answer
480 views

The Galois representation of a p-divisible group is crystalline

Can someone explain (or give a reference) why the Galois representation attached to a p-divisible group over the ring of integers of a p-adic ring is Crystalline?
12
votes
3answers
2k views

Dwork's use of p-adic analysis in algebraic geometry

Using p-adic analysis, Dwork was the first to prove the rationality of the zeta function of a variety over a finite field. From what I have seen, in algebraic geometry, this method is not used much ...