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Effective obstruction to lifting Tate classes from positive characteristic
Edgar Costa and Emre SertözAbstract
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.
- Received:
- 26.03.20
- Published:
- 26.03.20
Related publications
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)