Bloch's formula with modulus, ramified class field theory, and their applications

by Rahul Gupta (University of Regensburg)

Friday 25 Mar 2022, 11:30 → 13:30 Europe/Moscow

818-1526-4739 (Zoom)

Bloch's formula describes the Chow group of 0-cycles on a smooth quasi-projective scheme over a field in terms of the cohomology of the K-theory sheaves. In this talk, we shall discuss the meaning of Bloch's formula with modulus and focus on the formula for smooth projective varieties over finite fields. The main idea here is to study (and use) the higher dimension ramified geometric class field theory. We shall discuss various fundamental groups with modulus and how they are related to Bloch's formula with modulus. As an application, we shall prove the failure of Nisnevich descent for the Chow groups with modulus. This talk is based on joint works with Amalendu Krishna.