On Universal Norms for $p$-adic Representations in Higher Rank Iwasawa Theory

Dominik Bullach; Alexandre Daoud

On Universal Norms for $p$-adic Representations in Higher Rank Iwasawa Theory

Number Theory 2021-05-20 v2

Authors: Dominik Bullach , Alexandre Daoud

Abstract

We begin a systematic investigation of universal norms for $p$ -adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic pairing that is relevant to this setting. This allows us, for example, to refine the classical Iwasawa Main Conjecture for cyclotomic fields, and also to give applications to various well-known conjectures in arithmetic concerning Iwasawa invariants and leading terms of $L$ -functions.

Keywords

p-adic representations higher rank iwasawa theory universal norms iwasawa main conjecture l-functions

Cite

@article{arxiv.2007.07454,
  title  = {On Universal Norms for $p$-adic Representations in Higher Rank Iwasawa Theory},
  author = {Dominik Bullach and Alexandre Daoud},
  journal= {arXiv preprint arXiv:2007.07454},
  year   = {2021}
}

Comments

Manuscript revised according to referee report received

On Universal Norms for $p$-adic Representations in Higher Rank Iwasawa Theory

Abstract

Keywords

Cite

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