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 via YouTube
Overview
Syllabus
Intro
Setting the Stage
Local Systems on a Point
Analogue over K?
The Cyclotomic Character
Galois Representations from Geometry
Classical Hodge Theory
Hodge-Tate Representations
The Hodge-Tate Decomposition
Digression
Coherent Description of Étale Cohomology
Rigid-Analytic Description
Fundamental Calculation
The Riemann-Hilbert Correspondence of Lecture 2
The Functor RHC
p-adic Hodge Theory
The Classical Story
Example
The Comparison Conjecture
Sketch of Proof
Period Sheaves
Comparison with Coefficients
de Rham Local Systems
Taught by
Hausdorff Center for Mathematics
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Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 2
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Jacob Lurie: A Riemann-Hilbert Correspondence in P-Adic Geometry
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Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry
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Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry Part 1
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Hidden Structures on de Rham Cohomology of p-adic Analytic Varieties
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Constructible Sheaves and Filtered D-Modules
