Integral Frobenius for Abelian Varieties with Real Multiplication

Tommaso Giorgio Centeleghe () and Christian Theisen ()
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Tommaso Giorgio Centeleghe: IWR Universität Heidelberg
Christian Theisen: IWR Universität Heidelberg

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 147-175 from Springer

Abstract: Abstract In this paper we introduce the concept of integral Frobenius to formulate an integral analogue of the classical compatibility condition linking the collection of rational Tate modules V λ (A) arising from abelian varieties over number fields with real multiplication. Our main result gives a recipe for constructing an integral Frobenius when the real multiplication field has class number one. By exploiting algorithms already existing in the literature, we investigate this construction for three modular abelian surfaces over Q.

Keywords: Integral Tate module; Abelian variety; Real multiplication; 11G10; Abelian; varieties; of; dimension; >; 1 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_6

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DOI: 10.1007/978-3-319-70566-8_6

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