## Algebra

•  Romyar Sharifi, UCLA
•  Cocycles valued in motivic cohomology
•  10/09/2019
•  3:00 PM - 4:00 PM
•  C304 Wells Hall

I will describe joint work in progress with Akshay Venkatesh on the construction of 1-cocycles on $\mathrm{GL}_2(\mathbb{Z})$ valued in a limit of second motivic cohomology groups of open subschemes of the square of (1) the multiplicative group over the rationals and (2) a universal elliptic curve. I’ll explain how these cocycles specialize to homomorphisms taking modular symbols to special elements in second cohomology groups of cyclotomic fields and modular curves in the respective cases.

## Contact

Department of Mathematics
Michigan State University