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2021 | OriginalPaper | Chapter

Effective Obstruction to Lifting Tate Classes from Positive Characteristic

Authors : Edgar Costa, Emre Can Sertöz

Published in: Arithmetic Geometry, Number Theory, and Computation

Publisher: Springer International Publishing

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Abstract

We give an algorithm that takes a smooth hypersurface over a number field and computes a p-adic approximation of the obstruction map on the Tate classes of a finite reduction. This gives an upper bound on the “middle Picard number” of the hypersurface. The improvement over existing methods is that our method relies only on a single prime reduction and gives the possibility of cutting down on the dimension of Tate classes by two or more. The obstruction map comes from p-adic variational Hodge conjecture and we rely on the recent advancement by Bloch–Esnault–Kerz to interpret our bounds.
Footnotes
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This library is made available in SageMath [Sag20] through the wrapper https://​github.​com/​edgarcosta/​pycontrolledredu​ction.
 
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Metadata
Title
Effective Obstruction to Lifting Tate Classes from Positive Characteristic
Authors
Edgar Costa
Emre Can Sertöz
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-80914-0_9

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