The Galois action on symplectic K-theory

NUMBER THEORY

Speaker:

Tony Feng - MIT

A phenomenon underlying many remarkable results in number theory is the natural Galois action on the cohomology of symplectic groups of integers. In joint work with Soren Galatius and Akshay Venkatesh, we define a symplectic variant of algebraic K-theory, which carries a natural Galois action for similar reasons. We compute this Galois action and characterize it in terms of a universality property, in the spirit of the Langlands philosophy.