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In this article, we prove the non-existence of certain semistable Galois representations of a number field and apply our results 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.

Non-existence of Certain Galois Representations with a Uniform Tame Inertia Weight