Archived Events

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonne modules of abelian varieties defined over global function fields of characteristic p, combining methods of de Jong and Faltings. As a corollary we deduce that the monodromy groups of such overconvergent crystalline Dieudonne modules are reductive, and after base change to the field of complex numbers they are the same as the monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p.

We describe the recent research started by Nekrasov, Shatashvili, Braverman, Maulik, Okounkov on correspondence between the quantumcohomology of the quiver varieties and the quantum integrable systems. Our main example will be the quantum cohomology of the cotangent spaces to partial flag varieties and its vis a vis from the representation theory, the quasi periodic Heisenberg spin chain. We will discuss how the both subjects may contribute to each other via this correspondence.