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Kummer theory for products of one-dimensional tori Perissinotto, Flavio ; Perucca, Antonella in Publications Mathematiques de Besançon (in press) 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 ▲] Detailed reference viewed: 165 (43 UL)Kummer theory for multiquadratic or quartic cyclic number fields Perissinotto, Flavio ; Perucca, Antonella in Uniform distribution theory (2022), 17(no. 2), 165-194 Detailed reference viewed: 123 (16 UL)Kummer theory for finite fields and p-adic fields Perissinotto, Flavio ; Perucca, Antonella 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: 84 (4 UL)Three-dimensional arithmetic billiards Perucca, Antonella ; Perissinotto, Flavio ; E-print/Working paper (n.d.) Detailed reference viewed: 151 (5 UL)Galois groups of Kummer extensions of number fields Advocaat, Bryan ; Chan, Chi Wa ; Pajaziti, Antigona et al E-print/Working paper (n.d.) Detailed reference viewed: 54 (2 UL) |
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