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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
 abelian varieties
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Tag Archives: perfectoid things
Superfectoid spaces!?
Note (6/21): There is an issue with the proof of Lemma 1.7 below, but I’m pretty confident Kiran and I will find a fix. In any case, you should never take blog math too seriously! In this post I want to announce some … Continue reading
Posted in Math, Uncategorized
Tagged Kedlaya, padic geometry, perfectoid things, sousperfectoid spaces
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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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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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