A refined notion of arithmetically equivalent number fields, and curves with isomorphic Jacobians

2014/09/10 by Prasad, Dipendra · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1409.3173

Abstract

We construct examples of number fields which are not isomorphic but for which their idele class groups are isomorphic. We also construct examples of projective algebraic curves which are not isomorphic but for which their Jacobian varieties are isomorphic. Both are constructed using an example in group theory provided by Leonard Scott of a finite group G and subgroups H₁ and H₂ which are not conjugate in G but for which the G-module \mathbb Z[G/H₁] is isomorphic to \mathbb Z[G/H₂].

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• Classification of totally real number fields via their zeta function, regulator, and log unit lattice

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