Algebraic Geometry Seminar: "Algebraic representatives and intermediate Jacobians over perfect fields"

Abstract: Intermediate Jacobians and Abel-Jacobi maps provide a powerful tool for the study of complex projective manifolds. In positive characteristic, over algebraically closed fields, algebraic representatives and regular homomorphisms provide a replacement for the intermediate Jacobian and Abel-Jacobi map. I will discuss recent progress, with Jeff Achter and Charles Vial, extending this theory to the case of perfect fields, as well as some applications to a question of Barry Mazur on weight one Galois representations arising from geometry, and to integral decompositions of the diagonal.

Host: Matt Kerr