The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of

The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of

Explore the intricate world of overconvergent cohomology in Shimura varieties and its connection to p-adic automorphic forms in this 1-hour 7-minute lecture. Delve into the construction of eigenvarieties and the resulting coherent sheaf on rigid analytic spaces, examining how its cohomology relates to the finite slope part of overconvergent cohomology. Learn about a general conjecture for computing this coherent sheaf using stacks of Galois representations and understand its significance in the context of the p-adic Langlands program. Discover ongoing research with Zhixiang Wu that aims to prove this conjecture for modular curves, gaining insights into cutting-edge developments in algebraic geometry and number theory.