The Bloch-Kato Conjecture and Galois Theory

2010/12/27 by Dikran Karagueuzian, Karagueuzian, Dikran, John Labute +2
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1012.5631

Abstract

We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations, and their relationship with the Bloch-Kato conjecture proved by Rost and Voevodsky with Weibel's patch. Our main focus is on the third degree, but we provide examples for all degrees.

Related

• The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
• Bloch-Kato groups over perfectoid fields and Galois theory of p-adic periods
• Relations in the maximal pro-p quotients of absolute Galois groups
• Kato conjecture and motivic cohomology over finite fields
• Cohomology of absolute Galois groups