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Point counting on K3 surfaces and an application concerning real and complex multiplication

Published online by Cambridge University Press:  26 August 2016

Andreas-Stephan Elsenhans
Affiliation:
Mathematisches Institut, Universität Paderborn, Warburger Straße 100, D-33098 Paderborn, Germany email [email protected]
Jörg Jahnel
Affiliation:
Department Mathematik, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany email [email protected]

Abstract

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We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are $p$-adic in nature.

Type
Research Article
Copyright
© The Author(s) 2016 

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