Milnor K-groups attached to elliptic curves over a p-adic field

TL;DR

This paper investigates the Galois symbol map of Milnor K-groups linked to elliptic curves over p-adic fields and explores the structure of their Chow groups under certain conditions.

Contribution

It provides new insights into the structure of Milnor K-groups and Chow groups associated with elliptic curves over p-adic fields, including explicit descriptions.

Findings

Determined the structure of the Chow group for products of elliptic curves over p-adic fields.

Analyzed the Galois symbol map of Milnor K-groups attached to elliptic curves.

Provided conditions under which the structure results hold.

Abstract

We study the Galois symbol map of the Milnor $K$-group attached to elliptic curves over a $p$-adic field. As by-products, we determine the structure of the Chow group for the product of elliptic curves over a $p$-adic field under some assumptions.