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

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.Crown Copyright & COPY; 2023 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

We compute the algebraic K-theory of certain classes of surfaces over finite fields by calculating the motivic cohomology groups and studying the motivic Atiyah-Hirzebruch spectral sequence. In the appendix, we expand the scope of surfaces for which Parshin's conjecture is known to hold.