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Tag Archives: Weinstein
Perfectoid universal covers of curves
In a previous post I mumbled a bit about perfectoid covering spaces of rigid analytic varieties. In this post, I want to sketch a fun special case. Fix an algebraically closed nonarchimedean field. Recall the following from ScholzeWeinstein: given a … Continue reading
Posted in Math
Tagged Fresnel, Lutkebohmert, Matignon, padic geometry, perfectoid things, Pilloni, Scholze, Stroh, Weinstein
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The product of two diamonds
Let be the category of perfectoid spaces in characteristic , equipped with its proétale topology. Any gives rise to a sheaf on . By definition, a diamond is a sheaf on which admits a relatively representable surjection which pulls back … Continue reading
Posted in Math
Tagged GabberRamero, padic geometry, perfectoid things, Scholze, Weinstein
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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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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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