On a certain hypergeometric motive of weight 2 and rank 3

Bartosz Naskrecki

On a certain hypergeometric motive of weight 2 and rank 3

Number Theory 2017-05-19 v2 Algebraic Geometry

Authors: Bartosz Naskrecki

Abstract

We study a family of hypergeometric motives $H(\alpha,\beta|t)$ attached to a pair of tuples $\alpha=(1/4,1/2,3/4)$ , $\beta=(0,0,0)$ . To each such motive we can attach a system of $\ell$ --adic realisations with the trace of geometric Frobenius given by the evaluation of the finite field analogue of complex hypergeometric function. Geometry of elliptic fibrations makes it possible to to realise the motive $H(\alpha,\beta|t)$ as a pure Chow motive attached to a suitable K3 surface $V_{t}$ .

Keywords

hypergeometric motive Chow motive K3 surface elliptic fibration geometric Frobenius finite field

Cite

@article{arxiv.1702.07738,
  title  = {On a certain hypergeometric motive of weight 2 and rank 3},
  author = {Bartosz Naskrecki},
  journal= {arXiv preprint arXiv:1702.07738},
  year   = {2017}
}

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27 pages, 2 figures

On a certain hypergeometric motive of weight 2 and rank 3

Abstract

Keywords

Cite

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