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1
Intro
2
Setting the Stage
3
Local Systems on a Point
4
Analogue over K?
5
The Cyclotomic Character
6
Galois Representations from Geometry
7
Classical Hodge Theory
8
Hodge-Tate Representations
9
The Hodge-Tate Decomposition
10
Digression
11
Coherent Description of Étale Cohomology
12
Rigid-Analytic Description
13
Fundamental Calculation
14
The Riemann-Hilbert Correspondence of Lecture 2
15
The Functor RHC
16
p-adic Hodge Theory
17
The Classical Story
18
Example
19
The Comparison Conjecture
20
Sketch of Proof
21
Period Sheaves
22
Comparison with Coefficients
23
de Rham Local Systems
Description:
Explore the fifth installment of Jacob Lurie's lecture series on the Riemann-Hilbert correspondence in p-adic geometry. Delve into advanced mathematical concepts including local systems, Galois representations, Hodge theory, étale cohomology, and p-adic Hodge theory. Examine the cyclotomic character, Hodge-Tate decomposition, and the fundamental calculation leading to the Riemann-Hilbert correspondence. Investigate the comparison conjecture, period sheaves, and de Rham local systems. Gain insights into the classical story and its p-adic analogue, bridging geometric and algebraic perspectives in this 53-minute lecture from the Hausdorff Center for Mathematics.

Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry

Hausdorff Center for Mathematics
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#Mathematics #Hodge Theory #Number Theory #Galois Representations #p-adic Geometry
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Intro