Back to Algebraic Geometry Seminar: Spring 2025
Algebraic Geometry Seminar
Date: Wednesday, Jan 8, 2025
Time: 3:30PM - 4:30PM
Location: LCB 225
(joint with RT/NT) 2:00pm
Bogdan Zavyalov
Princeton University
Title |
Almost Coherent Sheaves and Poincaré Duality in p-adic Analytic Geometry |
Abstract |
In this work, we study étale cohomology of p-adic rigid-analytic spaces with F_p coefficients. For general (smooth) spaces, this cohomology theory does not behave so well. For example, F_p-cohomology groups of the 1-dimensional closed unit ball are infinite. Nevertheless, Scholze showed that H^i(X, F_p) are finite-dimensional for proper X. He further conjectured that these cohomology groups should satisfy Poincaré Duality when X is both smooth and proper. I will explain the proof of this conjecture using the concept of almost coherent sheaves that provides tools to “localize” the question in an appropriate sense and eventually reduce it to computations in group cohomology. |
Algebraic Geometry