Effective obstruction to lifting Tate classes from positive characteristic

Edgar Costa and Emre Sertöz

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Submission date: 26. Mar. 2020
Pages: 34
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
A recent result of Bloch-Esnault-Kerz describes the obstruction to formally lifting algebraic classes from positive characteristic to characteristic zero. We use their result to give an algorithm that takes a smooth hypersurface 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 it relies only on a single prime reduction and gives the possibility of cutting down on the dimension of Tate classes by two or more.