Integral elements of K-theory and products of modular curves II

TL;DR

This paper explores the concept of integrality in motivic cohomology and K-theory, establishing their equivalence in certain cases for products of curves and linking it to broader conjectures in arithmetic geometry.

Contribution

It proves the equivalence of different integrality notions in motivic cohomology/K-theory for products of curves and connects this to standard conjectures in arithmetic algebraic geometry.

Findings

Proved equivalence of integrality notions in specific cases

Reduced their equivalence to standard conjectures

Extended previous results to a general setting

Abstract

We discuss the relationship between different notions of "integrality" in motivic cohomology/K-theory which arise in the Beilinson and Bloch-Kato conjectures, and prove their equivalence in some cases for products of curves (used in the authors' previous paper in this series), as well as obtaining a general result, first proved by Jannsen (unpublished), which reduces their equivalence to standard conjectures in arithmetic algebraic geometry.