Notes on Étale Cohomology

ÉTALE COHOMOLOGY Contents

Comparison of Motivic and simplicial operations in mod-l-motivic and étale cohomology

In this paper we explore the relationships between the motivic and simplicial cohomology operations defined on mod-l motivic cohomology. We also explore similar relationships in étale cohomology and conclude by considering certain operations that commute with proper push-forwards.

ÉTALE COHOMOLOGY Contents

ÉTALE COHOMOLOGY Contents

THE Λ-ADIC EICHLER-SHIMURA ISOMORPHISM AND p-ADIC ÉTALE COHOMOLOGY

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