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2 votes
0 answers
110 views

Galois action on the cohomology of a curve over a local field with bad reduction

Let $C/\mathbb Q_p$ (or a p-adic local field more generally) be a smooth projective curve with split semistable reduction over $\mathbb Z_p$. What can we say about the action of the Galois group $\...
1 vote
0 answers
177 views

L-function in p-adic spaces

I've been learning more about different $p$-adic geometries, namely Berkovich spaces, Huber's Adic spaces and ridgid analytic spaces. In arithmetic geometry, it is often very interesting to assoicate ...
5 votes
0 answers
1k views

Formal GAGA and étale cohomology

Let $\mathfrak{X}$ be a $p$-adic flat formal scheme over $\mathbf{Z}_p$, whose special fiber has an ample line bundle. Then $\mathfrak{X}$ is algebraizable, that is there exists an algebraic $\mathbf{...