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1
Intro
2
Last Time
3
Computing the Riemann-Hilbert Functor
4
Beyond Characteristic p?
5
Perfection
6
Perfectoid Rings
7
Existence of Perfectoidizations
8
Perfectoidization with Compact Supports
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Relationship with the Riemann-Hilbert Functor
10
Perfected Prismatic Cohomology with Compact Supports
11
Extension to Derived Categories
12
Properties of the Riemann-Hilbert Functor
13
A Simplification
14
Example: Characteristic p
15
Anatomy of Sheaves
16
Sheaves on the Special Fiber
17
The Almost Category
18
Perfectoid Spaces
19
Recollections
20
Digression
21
Perfectoid Analogue
22
Comparison of Riemann-Hilbert Functors
23
Variant
Description:
Explore the intricacies of p-adic geometry in this advanced mathematics lecture on the Riemann-Hilbert correspondence. Delve into topics such as computing the Riemann-Hilbert functor, perfectoid rings, perfectoidization with compact supports, and prismatic cohomology. Examine the properties and simplifications of the Riemann-Hilbert functor, analyze sheaves on special fibers, and investigate perfectoid spaces. Compare different Riemann-Hilbert functors and gain insights into characteristic p examples and the almost category. This in-depth talk provides a comprehensive exploration of cutting-edge concepts in p-adic geometry for mathematicians and researchers in related fields.

Jacob Lurie: A Riemann-Hilbert Correspondence in P-Adic Geometry

Hausdorff Center for Mathematics
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