Finite generation conjectures for cohomology over finite fields

2011/03/29 by Thomas Geisser, Geisser, Thomas H
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1103.5544

openalex publication_date 2011/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an intermediate cohmology between motivic cohomology and Weil-etale cohomology. Using this, the Bass conjecture on finite generation of motivic cohomology, and the Beilinson-Tate on the finite generation of Weil-etale cohomology are related.

Citations

• Cohomological Hasse principle and motivic cohomology for arithmetic schemes

Related

• Weil-etale motivic cohomology
• Weil-etale cohomology over finite fields
• Weil cohomology theories and their motivic Hopf algebroids
• Kato conjecture and motivic cohomology over finite fields
• On extension of the motivic cohomology beyond smooth schemes