The analytic class number formula for $1$-dimensional affine schemes

Abstract

We derive an analytic class number formula valid for an order in a product of $S$-integers in global fields, or equivalently for reduced finite-type affine schemes of pure dimension $1$ over $\mathbb{Z}$.

15 pages; a second example, of a non-maximal order in a number field, was added. Some proofs are explained in more detail

References in corpus (1)

• Commensurability of automorphism groups

Cited by in corpus (2)

• Special values of $L$-functions on regular arithmetic schemes of dimension $1$
• Zeta-values of one-dimensional arithmetic schemes at strictly negative integers