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Two Lectures on the Arithmetic of K3 Surfaces

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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Part of the book series: Fields Institute Communications ((FIC,volume 67))

Abstract

In these lecture notes we review different aspects of the arithmetic of K3 surfaces. Topics include rational points, Picard number and Tate conjecture, zeta functions and modularity.

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Notes

  1. 1.

    Charles (to appear in Invent. Math.) and Madapusi Pera (arXiv: 1301.6326) have announced independent proofs of the Tate Conjecture for K3 surfaces outside characteristic 2 (and 3 in Charles’ case).

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Acknowledgements

It is a great pleasure to thank the other organisers of the Fields workshop and particularly all the participants for creating such a stimulating atmosphere. Special thanks to the Fields Institute for the great hospitality and to the referee for his comments. These lecture notes were written down while the author enjoyed support from the ERC under StG 279723 (SURFARI) which is gratefully acknowledged.

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  1. Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Matthias Schütt

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  1. Matthias Schütt
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Correspondence to Matthias Schütt .

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Editors and Affiliations

  1. , Mathematics Department, Stony Brook University, N/A, Stony Brook, 11794-3651, New York, USA

    Radu Laza

  2. , Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Matthias Schütt

  3. , Department of Math & Stats, Queen's University, University Ave., Kingston, K7L 3N6, Ontario, Canada

    Noriko Yui

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Schütt, M. (2013). Two Lectures on the Arithmetic of K3 Surfaces. In: Laza, R., Schütt, M., Yui, N. (eds) Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds. Fields Institute Communications, vol 67. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6403-7_3

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