Refined class number formulas for ${\mathbb{G}}_m$

Abstract

We formulate a generalization of a `refined class number formula' of Darmon. Our conjecture deals with Stickelberger-type elements formed from generalized Stark units, and has two parts: the `order of vanishing' and the `leading term'. Using the theory of Kolyvagin systems we prove a large part of this conjecture when the order of vanishing of the corresponding complex $L$-function is $1$.

Cited by in corpus (6)

• Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns
• On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group
• On derivatives of Kato's Euler system for elliptic curves
• On non-commutative Euler systems, I: preliminaries on `det' and `Fit'
• On a conjecture for Rubin-Stark elements in a special case
• Iwasawa theory and zeta elements for ${\mathbb{G}}_m$