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Perfectoid rings

Peter Scholze and Jared Weinstein

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

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter examines perfectoid spaces. A Huber ring R is Tate if it contains a topologically nilpotent unit; such elements are called pseudo-uniformizers. One can more generally define when an ... More


Examples of adic spaces

Peter Scholze and Jared Weinstein

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

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0004
Subject:
Mathematics, Geometry / Topology

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 ... More


Perfectoid spaces

Peter Scholze and Jared Weinstein

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

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter offers a second lecture on perfectoid spaces. A perfectoid Tate ring R is a complete, uniform Tate ring containing a pseudo-uniformizer. A perfectoid space is an adic space covered by ... More


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