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Mathematics > Algebraic Geometry

arXiv:1810.08644 (math)
[Submitted on 19 Oct 2018]

Title:The constant in the functional equation and derived extrior powers

Authors:Stephen Lichtenbaum
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Abstract:Let X be a regular scheme, projective and flat over the integers. Let A be the constant in the conjectured functional equation for the zeta-function of X. We give a conjecture computing A in terms of Euler characteristics of derived exterior powers of the sheaf of Kahler differentials on X, and prove this conjecture when the dimension of X is 1 or 2. This conjecture essentially says that the formulas for the special values of the zeta-function of X given by the author in a previous preprint are compatible with the functional equation.
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
Cite as: arXiv:1810.08644 [math.AG]
  (or arXiv:1810.08644v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1810.08644

Submission history

From: Stephen Lichtenbaum [view email]
[v1] Fri, 19 Oct 2018 18:54:37 UTC (6 KB)
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