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 Scholze-Weinstein: given a … Continue reading

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The product of two diamonds

Let be the category of perfectoid spaces in characteristic , equipped with its pro-étale 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

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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

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w-ordinary 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 p-adic fields. The definition is rather simple; the part which actually requires … Continue reading

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A p-divisible puzzle

Let be a completed algebraic closure of , and let be a p-divisible group. The Tate module of sits in a Hodge-Tate sequence . According to a recent theorem of Scholze-Weinstein, the map induces an equivalence of categories from the … Continue reading

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