On motivic cohomology with Z/l coefficients

TL;DR

This paper proves the Bloch-Kato conjecture, establishing a fundamental link between motivic cohomology and etale cohomology, thereby advancing understanding in algebraic geometry and number theory.

Contribution

It provides a corrected proof of the Bloch-Kato conjecture, clarifying the relationship between motivic and etale cohomology theories.

Findings

Proof of the Bloch-Kato conjecture established

Clarification of motivic and etale cohomology relationship

Correction of previous version of the proof

Abstract

In this paper we give a proof of the Bloch-Kato conjecture relating motivic cohomology and etale cohomology. It is a corrected version of the paper with the same title which posted earlier.