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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 geometry
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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Thoughts from Oberwolfach, Part I
Just back from a weeklong workshop at Oberwolfach on “Nonarchimedean geometry and applications”. Some random comments: During the workshop, Kiran Kedlaya started a nonarchimedean Scottish book, to record open problems in the foundations of nonarchimedean geometry, especially in the theory … Continue reading
Posted in Math
Tagged Ducros, Kato, Kedlaya, Lutkebohmert, Niziol, Oberwolfach, padic geometry
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It’s good to be spectral
Here’s a nice little theorem in rigid analytic geometry. Theorem. Let be an affinoid rigid space, with a closed analytic subset and an admissible open subset containing . Then for some , the “tube” around is contained in . To quote … Continue reading
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