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  1. Bog
  2. Geometri
  3. Algebraisk geometri

Berkeley Lectures on p-adic Geometry

Af: Jared Weinstein, Peter Scholze Engelsk Paperback

Berkeley Lectures on p-adic Geometry

Af: Jared Weinstein, Peter Scholze Engelsk Paperback
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Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field.

This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

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Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field.

This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 264
ISBN-13: 9780691202082
Indbinding: Paperback
Udgave:
ISBN-10: 0691202087
Kategori: Algebraisk geometri
Udg. Dato: 26 maj 2020
Længde: 17mm
Bredde: 234mm
Højde: 156mm
Forlag: Princeton University Press
Oplagsdato: 26 maj 2020
Forfatter(e): Jared Weinstein, Peter Scholze
Forfatter(e) Jared Weinstein, Peter Scholze

Kategori Algebraisk geometri

ISBN-13 9780691202082

Sprog Engelsk

Indbinding Paperback

Sider 264

Udgave

Længde 17mm

Bredde 234mm

Højde 156mm

Udg. Dato 26 maj 2020

Oplagsdato 26 maj 2020

Forlag Princeton University Press

Kategori sammenhænge