The Tate conjecture for \(K3\) surfaces over finite fields

DOI10.1007/S00222-012-0443-YzbMATH Open1282.14014arXiv1206.4002OpenAlexW2042542296WikidataQ29013677 ScholiaQ29013677MaRDI QIDQ378058

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Publication date: 11 November 2013

Published in: (Search for Journal in Brave)

Abstract: Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.

Full work available at URL: https://arxiv.org/abs/1206.4002

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