2-Adic point counting on K3 surfaces

2-Adic point counting on K3 surfaces

This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the 2-adic orthogonal group. Combining the new approach with a p -adic method, we count the number of points on some K 3 surfaces over the field F p , for all...

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Veröffentlicht in:Research in number theory 2022-12, Vol.8 (4), Article 85
Hauptverfasser: Elsenhans, Andreas-Stephan, Jahnel, Jörg
Format: Artikel
Sprache:eng
Schlagworte:
Fields (mathematics)
Fifteenth Algorithmic Number Theory Symposium (ANTS XV)
Mathematics
Mathematics and Statistics
Number Theory
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Zusammenfassung:This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the 2-adic orthogonal group. Combining the new approach with a p -adic method, we count the number of points on some K 3 surfaces over the field F p , for all primes p < 10 8 .
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-022-00378-x