Non-existence of certain Galois representations with a uniform tame inertia weight

TL;DR

This paper proves the non-existence of specific semistable Galois representations over number fields, with implications for geometric conjectures and finiteness results in algebraic geometry.

Contribution

It establishes new non-existence results for certain Galois representations, advancing understanding in number theory and related geometric problems.

Findings

Proves non-existence of certain semistable Galois representations

Applies results to a special case of Rasmussen and Tamagawa's conjecture

Implications for finiteness of abelian varieties with constrained torsion

Abstract

In this paper, we prove the non-existence of certain semistable Galois representations of a number field. Our consequence can be applied to some geometric problems. For example, we prove a special case of a Conjecture of Rasmussen and Tamagawa, related with the finiteness of the set of isomorphism classes of abelian varieties with constrained prime power torsion.