On 2-adic deformations

2015/09/01 by Paskunas, Vytautas
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1509.00320

Abstract

We compute the versal deformation ring of a split generic 2-dimensional representation χ₁⊕ χ₂ of the absolute Galois group of ℚ_p. As an application, we show that the Breuil--Mézard conjecture for both non-split extensions of χ₁ by χ₂ and χ₂ by χ₁ implies the Breuil--Mézard conjecture for χ₁⊕ χ₂. The result is new for p=2, the proof works for all primes.

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