## Geometry Seminar

**Date:** September 15, 2017

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 628

**Speaker:** Souvik Goswami, TAMU

**Title:** *Higher arithmetic Chow groups*

**Abstract:** For a regular scheme, which is flat and quasi-projective over an arithmetic ring (typically the ring of integers of a number field), Gillet and Soul ́e defined an arithmetic version of the usual Chow groups, taking into account the complex embeddings of the scheme. Typically the complex embeddings add more complex analytic/ Hodge-theoretic informations to the usual Chow groups. On the other hand, higher Chow groups were defined by Spencer Bloch as a simple example of a motivic cohomology. In this talk, we will explore the possibility to obtain a good definition for higher arithmetic Chow groups. This is a joint work with Jos ́e Ignacio Burgos from ICMAT, Madrid.