Zero-cycles on varieties over p-adic fields and Brauer groups

TL;DR

This paper investigates the Brauer-Manin pairing for varieties over p-adic fields, identifying the p-adic kernel component and computing zero-cycles on certain rational surfaces, advancing understanding of arithmetic geometry over local fields.

Contribution

It determines the p-adic part of the kernel of the Brauer-Manin pairing and computes zero-cycles on specific rational surfaces over p-adic fields, providing new insights into local arithmetic geometry.

Findings

Identified the p-adic kernel component of the Brauer-Manin pairing.

Computed the group of zero-cycles on a potentially rational surface.

Enhanced understanding of arithmetic properties of varieties over p-adic fields.

Abstract

In this paper, we study the Brauer-Manin pairing of smooth proper varieties over local fields, and determine the $p$-adic part of the kernel of one side. We also compute the $A_0$ of a potentially rational surface which splits over a wildly ramified extension.