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See detailKummer theory for products of one-dimensional tori
Perissinotto, Flavio UL; Perucca, Antonella UL

E-print/Working paper (n.d.)

Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated ... [more ▼]

Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated group of K-points on T. We show how to compute the degree of K(T[nt], (1/n)G) over K and how to determine whether T is split over such an extension. If K=Q, then we may compute at once the degree of the above extensions for all n and t. [less ▲]

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See detailKummer theory for multiquadratic or quartic cyclic number fields
Perissinotto, Flavio UL; Perucca, Antonella UL

E-print/Working paper (n.d.)

Detailed reference viewed: 91 (15 UL)
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See detailKummer theory for finite fields and p-adic fields
Perissinotto, Flavio UL; Perucca, Antonella UL

E-print/Working paper (n.d.)

Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N ... [more ▼]

Let K be a finite field or a finite extension of Qp for some prime number p. If G is a finitely generated subgroup of K*, then we can consider the degree of the cyclotomic-Kummer extension K(\zeta_N, \sqrt[n]{G})/K, where n divides N. If K is a finite field, then we give a closed formula for the degree, while if K is a p-adic field, then we describe a strategy to compute the degree. [less ▲]

Detailed reference viewed: 55 (1 UL)