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arXiv · 1909.07465

Special Values of the Zeta Function of an Arithmetic Surface

Matthias Flach·Daniel Siebel
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Abstract

We study the special value conjecture for the Zeta function of a proper regular arithmetic scheme X introduced by Flach and Morin in the case n=1. We compute the correction factor C(X,1) left unspecified in the original statement of the Flach-Morin Conjecture, thereby developing some results on the eh-topology introduced by Geisser. We then specialize further to the case where X is an arithmetic surface and show that the conjecture of Flach and Morin is equivalent to the Birch and Swinnerton-Dyer Conjecture.

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Matthias Flach, Daniel Siebel. 2019-09-16. Special Values of the Zeta Function of an Arithmetic Surface. https://doi.org/10.1017/s1474748021000104

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