  We study the special value conjecture for the Zeta function of a proper
regular arithmetic scheme X introduced by Flach and Morin in the case n=1. We
compute the correction factor C(X,1) left unspecified in the original statement
of the Flach-Morin Conjecture, thereby developing some results on the
eh-topology introduced by Geisser. We then specialize further to the case where
X is an arithmetic surface and show that the conjecture of Flach and Morin is
equivalent to the Birch and Swinnerton-Dyer Conjecture.
