An equivariant Iwasawa main conjecture for local fields

Abstract

Let $L/K$ be a finite Galois extension of $p$-adic fields and let $L_{\infty }$ be the unramified ${\mathbb{Z}}_p$-extension of $L$. Then $L_{\infty }/K$ is a one-dimensional $p$-adic Lie extension. In the spirit of the main conjectures of equivariant Iwasawa theory, we formulate a conjecture which relates the equivariant local epsilon constants attached to the finite Galois intermediate extensions $M/K$ of $L_{\infty }/K$ to a natural arithmetic invariant arising from the étale cohomology of the constant sheaf ${\mathbb{Q}}_p/{\mathbb{Z}}_p$ on the spectrum of $L_{\infty }$. We give strong evidence of the conjecture including a full proof in the case that $L/K$ is at most tamely ramified.

38 pages

Cited by in corpus (1)

• The epsilon constant conjecture for higher dimensional unramified twists of ${\mathbb{Z}}_p^r(1)$