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The Tate-Shafarevich groups of multinorm-one tori

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Publication:6331517

DOI10.1016/J.JPAA.2021.106906arXiv1912.09823MaRDI QIDQ6331517

Author name not available (Why is that?)

Publication date: 20 December 2019

Abstract: Let k be a global field and L be a finite dimensional 'etale algebra over k. In this paper, we assume that L is a product of cyclic extensions of k. Let T_{L/k} be the multinorm-one torus defined by the multinorm equation: N_{L/k} (t) = 1. Let X_c be the variety defined by the equation N_{L/k} (t) = c, for some c in k*. In this paper, we compute the Tate-Shafarevich group and the algebraic Tate-Shafarevich group of the character group of T_{L/k}. These groups measure the obstruction to the local-global principle for existence of rational points of X_c and the obstruction to the weak appraximation.





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