Variation of Néron-Severi ranks of reductions of K3 surfaces

Edgar Costa; Yuri Tschinkel

doi:10.1080/10586458.2014.947054

Variation of Néron-Severi ranks of reductions of K3 surfaces

Edgar Costa, Yuri Tschinkel

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 2¹⁶ in several representative examples and investigate the resulting statistics.

Original language	English (US)
Pages (from-to)	475-481
Number of pages	7
Journal	Experimental Mathematics
Volume	23
Issue number	4
DOIs	https://doi.org/10.1080/10586458.2014.947054
State	Published - Oct 2 2014

Keywords

K3 surfaces
Kedlaya's algorithm
Variation of Picard ranks
Variation of geometric Picard number

ASJC Scopus subject areas

Mathematics(all)

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10.1080/10586458.2014.947054

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title = "Variation of N{\'e}ron-Severi ranks of reductions of K3 surfaces",

abstract = "We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 216 in several representative examples and investigate the resulting statistics.",

keywords = "K3 surfaces, Kedlaya's algorithm, Variation of Picard ranks, Variation of geometric Picard number",

author = "Edgar Costa and Yuri Tschinkel",

note = "Funding Information: The first author was partially supported by FCT doctoral grant SFRH/BD/69914/2010. The second author was supported by National Science Foundation grants 0968318 and 1160859. Publisher Copyright: Copyright {\textcopyright} Taylor & Francis Group, LLC.",

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AU - Tschinkel, Yuri

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N2 - We study the behavior of geometric Picard ranks of K3 surfaces over Q under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 216 in several representative examples and investigate the resulting statistics.

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KW - Kedlaya's algorithm

KW - Variation of Picard ranks

KW - Variation of geometric Picard number

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Variation of Néron-Severi ranks of reductions of K3 surfaces

Abstract

Keywords

ASJC Scopus subject areas

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