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Mathematics > Number Theory

Title: 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 \'etale 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.
Comments: 38 pages
Subjects: Number Theory (math.NT)
Cite as: arXiv:1803.05743 [math.NT]
  (or arXiv:1803.05743v1 [math.NT] for this version)

Submission history

From: Andreas Nickel [view email]
[v1] Thu, 15 Mar 2018 13:38:27 GMT (44kb,D)