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Arithmetic of the [19,1,1,1,1,1] fibration

Matthias Schuett·Jaap Top
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Abstract

This paper studies the arithmetic of the extremal elliptic K3 surface with configuration of singular fibres [19,1,1,1,1,1]. We give a model over Q such that the Neron Severi group is generated by divisors over Q, and we describe the local Hasse-Weil zeta-functions in terms of a modular form of weight 3. Furthermore we verify the Tate conjecture for the reduction at 3 and comment on a conjecture of T. Shioda concerning the similarity of the lattice of transcendental cycles and a lattice resulting from supersingular reduction.

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Matthias Schuett, Jaap Top. 2005-10-04. Arithmetic of the [19,1,1,1,1,1] fibration. https://arxiv.org/abs/math/0510063

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