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I've been reading Kedlaya's paper http://arxiv.org/abs/math/0208027 on finiteness of rigid cohomology and there's something I can't quite resolve in my understanding of the topology on the Robba ring. …

To answer your second question, for any nilpotent neutral Tannakian category $\mathcal{C}$, (i.e. one in which every object is an iterated extension of the unit object $\underline{1}$), with fibre fun …

I am currently trying to understand intermediate extensions of perverse sheaves, specifically the proof of Gabber's purity theorem, which states that the intermediate extension of a pure perverse shea …

Suppose that $k$ is a perfect field of characteristic $p>0$, $\mathcal{V}$ is a complete discrete valuation ring with residue field $k$ and quotient field $K$, of characteristic $0$. Then when one d …

The Stacks Project has the following really nice Lemma concerning étale maps of rings: Let $A\rightarrow B$ be a finitely presented, étale morphism of rings. Then there exists a presentation $$ B\co …

This question is about 6 operations formalism for 'crystalline' cohomology theories - more specifically the infinitesimal cohomology of smooth $\mathbb{C}$-varieties, and the overconvergent cohomology …

So maybe everything I'm about to say you already know, so apologies if I'm teaching my grandmother to suck eggs. This is discussed a bit at the end of a paper of Fontaine "Representations $\ell$-adiq …

According to Wikipedia, a Weil cohomology theory is a functor from the category of smooth projective varieties over a field $k$, to graded algebras over a field $K$ of characteristic zero, together wi …

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 fo …

Suppose that $X/\mathbb{Q}_p$ is a smooth, projective variety, and choose a prime $\ell\neq p$. Then the weight-monodromy conjecture says that the graded pieces $\mathrm{Gr}_k^M$ of the monodromy filt …