Motivic cohomology and algebraic K-theory of some surfaces over finite fields

2023/02/20 by Oliver Gregory, Gregory, Oliver
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2302.09867

Abstract

We compute the algebraic K-theory of some classes of surfaces defined over finite fields. We achieve this by first calculating the motivic cohomology groups and then studying the motivic Atiyah-Hirzebruch spectral sequence. In an appendix, we slightly enlarge the class of surfaces for which Parshin's conjecture is known.

Related

• Parshin's conjecture and motivic cohomology with compact support
• Motivic cohomology of equicharacteristic schemes
• Algebraic K-Theory
• Kato conjecture and motivic cohomology over finite fields
• Constructing Indecomposable Motivic Cohomology Classes on Algebraic Surfaces