2021/12/24 by S. Aniruddha, Aniruddha, S., Jyoti Prakash Saha +1
Computer Science · Mathematics · #Coding theory and cryptography #Algebraic Geometry and Number Theory #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2112.13051
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.