For an abelian variety A over an algebraically closed non-archimedean field of residue characteristic p, we show that there exists a perfectoid space which is the tilde-limit of lim ← −[p] A.Our proof also works for the larger class of abeloid varieties.
We provide a simple approach for the crystalline comparison of A inf -cohomology, and reprove the comparison between crystalline and p-adic étale cohomology for formal schemes in the case of good reduction.
This article generalizes the geometric quadratic Chabauty method, initiated over
Q
\mathbb {Q}
by Edixhoven and Lido, to curves defined over arbitrary number fields. The main result is a conditional bound on the number of rational points on curves that satisfy an additional Chabauty type condition on the Mordell–Weil rank of the Jacobian. The method gives a more direct approach to the generalization by Dogra of the quadratic Chabauty method to arbitrary number fields.
We use the Nygaard filtration on Ainf cohomology to give a new proof of the following result: for a smooth proper (formal) scheme over a mixed characteristic valuation ring, the Newton polygon of its special fiber lies on or above the Hodge polygon of its generic fiber.
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