Characteristic Classes of Étale Local Systems

Explore a lecture on the characteristic classes of étale Z_p-local systems on algebraic varieties. Delve into how continuous cohomology classes of GL_n(Z_p) give rise to classes in étale cohomology with Z_p coefficients. Compare these characteristic classes to p-adic analogs of Chern-Simons classes for flat vector bundles. Examine Reznikov's theorem on torsion of Chern-Simons classes for C-local systems on complex projective varieties. Discover how étale Z_p-local system classes on non-closed field varieties can be non-zero rationally. Investigate the relationship between characteristic classes and Chern classes of Hodge filtration quotients for de Rham local systems on p-adic field varieties. Learn about an analog of Chern classes for pro-étale site vector bundles. This lecture, presented by Alexander Petrov from Harvard University, covers joint work with Lue Pan and is available on the CARMIN.tv platform, which offers additional features for the research community.