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arithmetica on Superfectoid spaces!? arithmetica on Superfectoid spaces!? mayorliatmath on Superfectoid spaces!? lucqin on Superfectoid spaces!? Jesse on Fun with crystalline peri… Tags
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Tag Archives: padic Hodge theory
Period morphisms in padic Hodge theory
In classical Hodge theory, variations of Hodge structure give rise to varying periods, and then to period morphisms. In padic Hodge theory, there are plenty of periods but (until recently) not so many period morphisms. It turns out these exist … Continue reading
Posted in Math, Uncategorized
Tagged padic geometry, padic Hodge theory, perfectoid things
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Local gamma factors and padic Lfunctions
(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
Posted in Math
Tagged Berger, Coates, padic Hodge theory, padic Lfunctions, PerrinRiou
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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
Posted in Math
Tagged Colmez, Fargues, Fontaine, padic Hodge theory, perfectoid things, Scholze, Weinstein
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Halloween twoforone 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
Posted in Math
Tagged BreuilSchneider conjecture, padic Hodge theory, padic Langlands, perfectoid things
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HodgeTate proliferation
Let be a complete algebraically closed extension, and let be an abelian variety, with padic Tate module and dual abelian variety . There are then at least three natural candidates for a “HodgeTate map” To wit: 1. (Scholze) For any … Continue reading
Posted in Math
Tagged abelian varieties, Coleman, Fargues, padic Hodge theory, pdivisible groups, Scholze, Tate
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wordinary 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 padic fields. The definition is rather simple; the part which actually requires … Continue reading
Posted in Math
Tagged abelian varieties, Fargues, overconvergent modular forms, padic Hodge theory, Pilloni, Scholze, Shimura varieties, Weinstein
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A pdivisible puzzle
Let be a completed algebraic closure of , and let be a pdivisible group. The Tate module of sits in a HodgeTate sequence . According to a recent theorem of ScholzeWeinstein, the map induces an equivalence of categories from the … Continue reading
Posted in Uncategorized
Tagged padic Hodge theory, pdivisible groups, Scholze, Weinstein
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