A Base Change Version of Rasmussen-Tamagawa Conjecture

2022/08/08 by Das, Plawan, Sarkar, Subham
#11F80 #11G05 #11G10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.04170

Abstract

We prove a certain uniform version of the Shafarevich Conjecture. As a corollary, we prove the Rasmussen-Tamagawa Conjecture for a particular class of abelian varieties A defined over a number K of dimension g having everywhere potential good reduction, in particular, for any finite place v of K the localization A_v:=A×_Spec(K)Spec(K_v) has either good reduction or \it totally bad reduction (connected component A_v⁰ of the special fibre A_v of the Néron model A_v at v is an affine group scheme over the residue field k_v at v) and has good reduction over a quadratic extension of K_v.

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