The Galois action on symplectic K-theory

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, September 17, 2019 - 4:15pm
Location: 
LOM 205
Speaker: 
Tony Feng
Speaker affiliation: 
Massachusetts Institute of Technology
Event description: 

Abstract: A fundamental principle in number theory is that the cohomology of locally symmetric spaces carries interesting Galois representations. However, locally symmetric spaces are also associated with other kinds of algebraic invariants, such as algebraic K-theory, and one could also try to study the Galois action on them. In joint work with Soren Galatius and Akshay Venkatesh, we define a symplectic version of algebraic K-theory for the integers, and compute the Galois action on it. The proofs use the fundamental theorem of complex multiplication and the fundamental theorem of hermitian K-theory.