Wild Galois Representations: Elliptic curves over a $3$-adic field

Coppola, Nirvana

doi:10.48550/arxiv.1812.05651

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2020

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“…As explained in [1], the representation described here is the dual of the representation on the étale cohomology of E. In particular the function GaloisRepresentation implemented in MAGMA computes the Galois representation on the étale cohomology. Concretely, the two only differ by the character value of ψ on the elements of the two conjugacy classes 8A and 8B.…”

Section: Final Considerationsmentioning

confidence: 99%

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Wild Galois representations: Elliptic curves over a 2-adic field with non-abelian inertia action

Coppola

2020

Int. J. Number Theory

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In this paper we present a description of the Galois representation attached to an elliptic curve defined over a 2-adic field K, in the case where the image of inertia is non-abelian. There are two possibilities for the image of inertia, namely Q 8 and SL 2 (F 3 ), and in each case we need to distinguish whether the inertia degree of K over Q 2 is even or odd. The result presented here can be implemented in an algorithm to compute explicitly the Galois representation in these four cases.

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Section: Final Considerationsmentioning

confidence: 99%

“…Theorem 1 and Theorems 3.1 and 3.2 of [1] give a method to describe completely the Galois representation of an elliptic curve with potential good reduction and non-abelian inertia action. The cases where the image of inertia is cyclic are dealt with in [4].…”

Section: Final Considerationsmentioning

confidence: 99%

Wild Galois representations: Elliptic curves over a 2-adic field with non-abelian inertia action

Coppola

2020

Int. J. Number Theory

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Wild Galois Representations: Elliptic curves over a $3$-adic field

Cited by 1 publication

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Wild Galois representations: Elliptic curves over a 2-adic field with non-abelian inertia action

Wild Galois representations: Elliptic curves over a 2-adic field with non-abelian inertia action

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