Eisenstein cocycles in motivic cohomology

Abstract: I will describe joint work with Akshay Venkatesh on the construction of GL_2(Z)-cocycles valued in second K-groups of the function fields of the squares of the multiplicative group over the rationals and a universal elliptic curve. Focusing on the first case, I’ll explain how the cocycle we construct specializes to homomorphisms taking modular symbols for congruence subgroups to special elements in second cohomology groups of cyclotomic fields and satisfies a certain property of being “Eisenstein”.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar