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2020 On a cohomological generalization of the Shafarevich conjecture for K3 surfaces
Teppei Takamatsu
Algebra Number Theory 14(9): 2505-2531 (2020). DOI: 10.2140/ant.2020.14.2505

Abstract

The Shafarevich conjecture for K3 surfaces asserts the finiteness of isomorphism classes of K3 surfaces over a fixed number field admitting good reduction away from a fixed finite set of finite places. André proved this conjecture for polarized K3 surfaces of fixed degree, and recently She proved it for polarized K3 surfaces of unspecified degree. We prove a certain generalization of their results, which is stated by the unramifiedness of -adic étale cohomology groups for K3 surfaces over finitely generated fields of characteristic 0. As a corollary, we get the original Shafarevich conjecture for K3 surfaces without assuming the extendability of polarization, which is stronger than the results of André and She. Moreover, as an application, we get the finiteness of twists of K3 surfaces via a finite extension of characteristic 0 fields.

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Teppei Takamatsu. "On a cohomological generalization of the Shafarevich conjecture for K3 surfaces." Algebra Number Theory 14 (9) 2505 - 2531, 2020. https://doi.org/10.2140/ant.2020.14.2505

Information

Received: 15 October 2019; Revised: 11 March 2020; Accepted: 11 May 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172714
Digital Object Identifier: 10.2140/ant.2020.14.2505

Subjects:
Primary: 14J28
Secondary: 11F80, 11G18, 11G25, 11G35

Rights: Copyright © 2020 Mathematical Sciences Publishers

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