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arXiv · 1810.08644

The constant in the functional equation and derived extrior powers

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.

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Stephen Lichtenbaum. 2018-10-19. The constant in the functional equation and derived extrior powers. https://arxiv.org/abs/1810.08644

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