On some local properties of sequences of big Galois representations

S. Aniruddha; Jyoti Prakash Saha

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arXiv · 2112.13051

On some local properties of sequences of big Galois representations

S. Aniruddha·Jyoti Prakash Saha

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Abstract

In this article, we prove that for a convergent sequence of residually absolutely irreducible representations of the absolute Galois group of a number field $F$ with coefficients in a domain finite over a power series ring over a $p$-adic integer ring, the set of places of $F$ where some of the representations ramifies has density zero. Using this, we extend a result of Das--Rajan to such convergent sequences. We also establish a strong multiplicity one theorem for big Galois representations.

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S. Aniruddha, Jyoti Prakash Saha. 2021-12-24. On some local properties of sequences of big Galois representations. https://arxiv.org/abs/2112.13051

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