Tag Archives: p-adic Hodge theory

Period morphisms in p-adic Hodge theory

In classical Hodge theory, variations of Hodge structure give rise to varying periods, and then to period morphisms.  In p-adic Hodge theory, there are plenty of periods but (until recently) not so many period morphisms.  It turns out these exist … Continue reading

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Local gamma factors and p-adic L-functions

(Usual pedantry: Fix a prime , , , etc. For any finite over let denote the maximal unramified subfield, and write , , as usual. Set for any , with its natural actions of and .) Let be a number … Continue reading

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Diamonds in the rough

This post is an outgrowth of my (ongoing) attempt to understand Peter Scholze’s remarkable course at Berkeley.  The first couple of paragraphs below are a rather comically compressed summary of some portions of Jared Weinstein’s excellent notes (though of course all mistakes are my … Continue reading

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Halloween two-for-one sale

In a previous post, I asked the following question: Let be a finite extension of with uniformizer , , (resp. ) the upper (resp. lower) triangular Borel, the diagonal maximal torus. Fix another finite extension , and let be a … Continue reading

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Hodge-Tate proliferation

Let be a complete algebraically closed extension, and let be an abelian variety, with p-adic Tate module and dual abelian variety . There are then at least three natural candidates for a “Hodge-Tate map” To wit: 1. (Scholze) For any … Continue reading

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w-ordinary abelian varieties and their moduli

(This post describes ongoing joint work with Przemyslaw Chojecki and Christian Johansson.) In this post I want to describe a new gauge for the ordinarity of abelian varieties over p-adic fields. The definition is rather simple; the part which actually requires … Continue reading

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A p-divisible puzzle

Let be a completed algebraic closure of , and let be a p-divisible group. The Tate module of sits in a Hodge-Tate sequence . According to a recent theorem of Scholze-Weinstein, the map induces an equivalence of categories from the … Continue reading

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