Peter Scholze and Jared Weinstein
- 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 ...
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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 affinoid adic spaces with R perfectoid. The term “affinoid perfectoid space” is ambiguous. The chapter then looks at the tilting process and the tilting equivalence. The tilting equivalence extends to the étale site of a perfectoid space. Why is it important to study perfectoid spaces? The chapter puts forward a certain philosophy which indicates that perfectoid spaces may arise even when one is only interested in classical objects.Less
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 affinoid adic spaces with R perfectoid. The term “affinoid perfectoid space” is ambiguous. The chapter then looks at the tilting process and the tilting equivalence. The tilting equivalence extends to the étale site of a perfectoid space. Why is it important to study perfectoid spaces? The chapter puts forward a certain philosophy which indicates that perfectoid spaces may arise even when one is only interested in classical objects.
