Values of zeta functions of arithmetic surfaces at $s=1$

Abstract

We show that the recent conjecture of the first-named author for the special value at $s=1$ of the zeta function of an arithmetic surface is equivalent to the Birch-Swinnerton-Dyer conjecture for the Jacobian of the generic fibre.

29 pages; revised version following suggestions of referee; to appear in JIMJ (Journal of the Institute of Mathematics of Jussieu)

References in corpus (2)

• Special Values of the Zeta Function of an Arithmetic Surface
• The conjectures of Artin-Tate and Birch-Swinnerton-Dyer