P-adic heights and p-adic Hodge theory

TL;DR

This paper develops a framework for p-adic heights of p-adic representations using $(,)$-modules and Selmer complexes, advancing p-adic Hodge theory and its applications.

Contribution

It introduces a new construction of p-adic heights for representations with coefficients in affinoid algebras, integrating $(,)$-modules and Selmer complexes.

Findings

Constructed p-adic height pairing for p-adic representations.

Extended p-adic Hodge theory to include affinoid algebra coefficients.

Provided new tools for studying arithmetic properties of p-adic Galois representations.

Abstract

Using the theory of $(\phi,\Gamma)$-modules and the formalism of Selmer complexes we construct the p-adic height for p-adic representations with coefficients in an affinoid algebra over $Q_p$.