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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: Scholze
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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Perfectoid uniformization, part one (ed.: and part two)
Let be a complete algebraically closed extension of , and let be a nice rigid analytic space/locally Noetherian adic space over . What should it mean for to be covered by a perfectoid space? Here’s one possible definition: Definition. A perfectoid covering space of is … Continue reading
A remark on sheafy Huber rings
Let be a (complete) Huber ring, i.e. a complete topological ring containing an open subring which is adic with respect to a finitely generated ideal of definition . A Huber ring is Tate if contains a topologically nilpotent unit ; … Continue reading
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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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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Some little remarks on big Hecke algebras
Edit (7/22): The second paragraph in the proof of the proposition below is total nonsense. I’ll put up a second version of this post soon, but I’m leaving the original as a warning to myself to not write blog posts when … Continue reading