Values of zeta functions of arithmetic surfaces at $s=1$
Algebraic Geometry
2022-03-28 v2 Number Theory
Abstract
We show that the recent conjecture of the first-named author for the special value at of the zeta function of an arithmetic surface is equivalent to the Birch-Swinnerton-Dyer conjecture for the Jacobian of the generic fibre.
Keywords
Cite
@article{arxiv.2101.06530,
title = {Values of zeta functions of arithmetic surfaces at $s=1$},
author = {S. Lichtenbaum and N. Ramachandran},
journal= {arXiv preprint arXiv:2101.06530},
year = {2022}
}
Comments
29 pages; revised version following suggestions of referee; to appear in JIMJ (Journal of the Institute of Mathematics of Jussieu)