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Corpus ID: 214641174

Effective obstruction to lifting Tate classes from positive characteristic

@article{Costa2020EffectiveOT,
title={Effective obstruction to lifting Tate classes from positive characteristic},
author={Edgar Costa and Emre Can Sertoz},
journal={arXiv: Algebraic Geometry},
year={2020}
}

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… Expand