The Lambda-adic Eichler-Shimura isomorphism and p-adic etale cohomology

TL;DR

This paper provides a new proof of Ohta's Lambda-adic Eichler-Shimura isomorphism by leveraging p-adic Hodge theory and recent advances in p-adic etale cohomology, enhancing understanding of p-adic Galois representations.

Contribution

The paper introduces a novel proof of the Lambda-adic Eichler-Shimura isomorphism utilizing p-adic Hodge theory and recent cohomological results, offering new insights into p-adic Galois representations.

Findings

New proof of Lambda-adic Eichler-Shimura isomorphism

Application of p-adic Hodge theory to cohomology

Connections with Bloch-Kato and Hyodo results

Abstract

We give a new proof of Ohta's Lambda-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic etale cohomology.