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MiS Preprint

Effective obstruction to lifting Tate classes from positive characteristic

Edgar Costa and Emre Sertöz


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.


Related publications

2021 Repository Open Access
Edgar Costa and Emre Can Sertöz

Effective obstruction to lifting Tate classes from positive characteristic

In: Arithmetic geometry, number theory, and computation / Jennifer S. Balakrishnan (ed.)
Cham : Springer, 2021. - pp. 293-333
(Simons Symposia)