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arXiv · 2012.05483

Specialization maps for Scholze's category of diamonds

Ian Gleason
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Abstract

We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an etale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified p-adic Beilinson--Drinfeld Grassmannians are kimberlites with finiteness and normality properties.

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Ian Gleason. 2020-12-10. Specialization maps for Scholze's category of diamonds. https://arxiv.org/abs/2012.05483

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