4
votes
0answers
96 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 ...
5
votes
0answers
422 views

a naive question about p-adic local monodromy theorem

The question is about whether one can view the p-adic local monodromy theorem as the quasi-unipotence of some monodromy operator. it is known that the classical local monodromy theorem (i.e. for ...
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
482 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?
5
votes
2answers
852 views

Direct proof of special case of Hasse's theorem for elliptic curves

Consider the elliptic curve $y^2 = x^3 + x$ over $\mathbb{F}_p$, where $p \equiv 1 \pmod 4$. If memory serves correctly, the number of points (excluding the point at infinity) is $p - a$ where $a$ is ...
5
votes
1answer
619 views

bibl. q.s on Dwork's “p-adic cycles”, Mazur's “p-adic variations”:

Matthew Emerton mentioned recently the relevance of Dwork's "p-adic cycles". As I wonder if I should read that, reviews of it are ambiguous, I'd be happy on remarks and possible further bibl. hints. ...