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arXiv · 2302.09867

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

Oliver Gregory
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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.

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Oliver Gregory. 2023-02-20. Motivic cohomology and algebraic $K$-theory of some surfaces over finite fields. https://arxiv.org/abs/2302.09867

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