The constant in the functional equation and derived extrior powers

2018/10/19 by Stephen Lichtenbaum, Lichtenbaum, Stephen · 1 citation
Chemistry · Mathematics · #Algebraic Geometry (math.AG) #Analytical Chemistry and Chromatography #Chemical Thermodynamics and Molecular Structure #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1810.08644

openalex publication_date 2018/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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