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

Examples of adic spaces

(p.27) Lecture 4 Examples of adic spaces
Berkeley Lectures on p-adic Geometry

Peter Scholze

Jared Weinstein

Princeton University Press

This chapter discusses various examples of adic spaces. These examples include the adic closed unit disc; the adic affine line; the closure of the adic closed unit disc in the adic affine line; the open unit disc; the punctured open unit disc; and the constant adic space associated to a profinite set. The chapter focuses on one example: the adic open unit disc over Zp. The adic spectrum Spa Zp consists of two points, a special point and a generic point. The chapter then studies the structure of analytic points. It also clarifies the relations between analytic rings and Tate rings.

Keywords:   adic spaces, adic closed unit disc, adic affine line, adic open unit disc, adic spectrum, analytic points, analytic rings, Tate rings

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