• Corpus ID: 119642455

# Special Values of Zeta Functions of Schemes

@article{Lichtenbaum2017SpecialVO,
title={Special Values of Zeta Functions of Schemes},
author={Stephen Lichtenbaum},
journal={arXiv: Algebraic Geometry},
year={2017}
}
• S. Lichtenbaum
• Published 31 March 2017
• Mathematics
• arXiv: Algebraic Geometry
Let X be a regular scheme, projective and flat over Spec \mathbb Z. We give two conjectural formulas, 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. The first formula builds on work of Fontaine and Perrin-Riou replacing \mathbb Q_structuers by \mathbb Z-structures, and the second is a very simple formula in terms of the Euler characteristic of a certain complex of sheaves in a hypothetical Weil-etale Grothendieck topology. A…
Following the ideas of Flach and Morin [11], we state a conjecture in terms of Weil-étale cohomology for the vanishing order and special value of the zeta function ζ(X, s) at s = n < 0, where X is a
Following the ideas of Flach and Morin [FM2018], we state a conjecture in terms of Weil-étale cohomology for the vanishing order and special value of the zeta function ζ(X, s) at s = n < 0, where X
Let X be an arithmetic scheme (i.e., separated, of finite type over SpecZ) of Krull dimension 1. For the associated zeta function ζ(X, s), we write down a formula for the special value at s = n < 0
We construct the Weil-\'etale cohomology and Euler characteristics for a subclass of the class of $\mathbb{Z}$-constructible sheaves on the spectrum of the ring of integers of a totally imaginary

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