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arXiv · 1704.00062

Special Values of Zeta Functions of Schemes

Stephen Lichtenbaum
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Abstract

Let X be a regular scheme, projective and flat over Spec \mathbb Z. We give a conjectural formula, up to sign and powers of 2, for \zeta^*(X,r), the leading term in the series expansion of \zeta(X,s) at s=r, in terms of Weil-etale motivic cohomology, singular cohomology, and derived de Rham cohomology. This formula builds on work of Fontaine and Perrin-Riou replacing \mathbb Q_structuers by \mathbb Z-structures. We show that our conjectured formula is compatible with Serre's functional equation for the zeta function of X.

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Stephen Lichtenbaum. 2017-03-31. Special Values of Zeta Functions of Schemes. https://arxiv.org/abs/1704.00062

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