The strong Stark conjecture for totally odd characters

Abstract

We prove the $p$-part of the strong Stark conjecture for every totally odd character and every odd prime $p$. Let $L/K$ be a finite Galois CM-extension with Galois group $G$, which has an abelian Sylow $p$-subgroup for an odd prime $p$. We give an unconditional proof of the minus $p$-part of the equivariant Tamagawa number conjecture for the pair $(h^0(\mathrm{Spec}(L)), \mathbb{Z}[G])$ under certain restrictions on the ramification behavior in $L/K$.

Theorems & Definitions (25)

• Theorem 1
• Corollary 1
• Theorem 2
• Corollary 2
• Conjecture 1.1: Stark
• Remark 1.2
• Theorem 1.3: Siegel
• Remark 1.4
• Conjecture 1.5: Strong Stark
• Proposition 1.6