Fields of definition of K3 surfaces with complex multiplication

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  • Domenico Valloni

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Original languageEnglish
Pages (from-to)436-470
Number of pages35
JournalJournal of number theory
Volume242
Early online date25 May 2022
Publication statusPublished - Jan 2023

Abstract

Let X/C be a K3 surface with complex multiplication by the ring of integers of a CM field E. We show that X can always be defined over an Abelian extension K/E explicitly determined by the discriminant form of the lattice NS(X). We then construct a model of X over K via Galois-descent and we study some of its basic properties, in particular we determine its Galois representation explicitly. Finally, we apply our results to give upper and lower bounds for a minimal field of definition for X in terms of the class number of E and the discriminant of NS(X).

Keywords

    Class field theory, Complex multiplication, Fields of definition, K3 surfaces

ASJC Scopus subject areas

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Fields of definition of K3 surfaces with complex multiplication. / Valloni, Domenico.
In: Journal of number theory, Vol. 242, 01.2023, p. 436-470.

Research output: Contribution to journalArticleResearchpeer review

Valloni D. Fields of definition of K3 surfaces with complex multiplication. Journal of number theory. 2023 Jan;242:436-470. Epub 2022 May 25. doi: 10.48550/arXiv.1907.01336, 10.1016/j.jnt.2022.04.013
Valloni, Domenico. / Fields of definition of K3 surfaces with complex multiplication. In: Journal of number theory. 2023 ; Vol. 242. pp. 436-470.
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