• Corpus ID: 119642455

Special Values of Zeta Functions of Schemes

  title={Special Values of Zeta Functions of Schemes},
  author={Stephen Lichtenbaum},
  journal={arXiv: Algebraic Geometry},
  • 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… 

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