La conjecture $\epsilon$ locale de Kato en dimension $2$

Joaquín Rodrigues Jacinto

La conjecture $\epsilon$ locale de Kato en dimension $2$

Number Theory 2018-02-19 v2

Authors: Joaquín Rodrigues Jacinto

Abstract

We show an Iwasawa functional equation for a two dimensional $p$ -adic representation of the absolute Galois group of $\mathbf{Q}_p$ . This allows us to complete Nakamura's proof of Kato's local $\epsilon$ -conjecture in dimension $2$ .

Keywords

Kato's local ε-conjecture Iwasawa functional equation p-adic representations absolute Galois group dimension 2 Nakamura's proof

Cite

@article{arxiv.1702.05637,
  title  = {La conjecture $\epsilon$ locale de Kato en dimension $2$},
  author = {Joaquín Rodrigues Jacinto},
  journal= {arXiv preprint arXiv:1702.05637},
  year   = {2018}
}

Comments

28 pages, submitted. In french. Several small modifications following the referees comments. Section 2.4 completely changed. To appear in Mathematische Annalen

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