Perfectoid and prismatic methods

MATH-706 / 3 credits

Teacher: Patakfalvi Zsolt

Language: English

Remark: This is an algebraic geometry PhD course about perfectoid and prismatic methods.

Frequency

Only this year

Summary

Contents: mixed characteristic geometry, perfectoid rings, primsatic cohomology and their applications to Kodaira type vanishing theorems.

Content

The topic is mixed characteristic algebraic geometry, more precisely, studying perfectoid rings, prismatic cohomology and some of their applications. We will follow parts of Bhatt's lectures on "Prismatic F-Gauges" and "Aspects of p-adic hodge theory". Among one of the goals is to understand the proof of vanishing theorems in mixed characteristic in detail. Another is to understand precisely prismatic cohomology and perfectoid rings.

Learning Prerequisites

Required courses

MATH 510 - Algebraic geometry II - schemes and sheaves

 

Recommended courses

MATH 535 - Algebraic geometry III - selected topics

Resources

Bibliography

Bhatt's lectures on "Prismatic F-Gauges" and "Aspects of p-adic hodge theory"

Moodle Link

In the programs

  • Exam form: Term paper (session free)
  • Subject examined: Perfectoid and prismatic methods
  • Courses: 28 Hour(s)
  • Project: 28 Hour(s)
  • Type: optional

Reference week

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