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Berkeley Lectures on p-adic Geometry(AMS-207)$
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Berkeley Lectures on p-adic Geometry: (AMS-207)

Peter Scholze and Jared Weinstein

Print publication date: 2020

Print ISBN-13: 9780691202082

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691202082.001.0001

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Examples of diamonds

Examples of diamonds

Chapter:
(p.131) Lecture 15 Examples of diamonds
Source:
Berkeley Lectures on p-adic Geometry
Author(s):

Peter Scholze

Jared Weinstein

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691202082.003.0015

This chapter assesses some interesting examples of diamonds. So far, the only example encountered is the self-product of copies of Spd Qp. The chapter first studies this self-product. It is useful to keep in mind that a diamond can have multiple “incarnations.” Another important class of diamonds, which in fact were one of the primary motivations for their definition, is the category of Banach-Colmez spaces. Recently, le Bras has reworked their theory in terms of perfectoid spaces. The category of Banach-Colmez spaces over C is the thick abelian subcategory of the category of pro-étale sheaves of Qp-modules. This is similar to a category considered by Milne in characteristic p.

Keywords:   diamonds, self-product, incarnations, Banach-Colmez spaces, perfectoid spaces, abelian subcategory, pro-étale sheaves

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