On Kummer ectensions generated by S-units in algebraic number fields

— Algebraic curves, finite fields, rational points, genus, linear codes, asymp- totics, tower of curves.. The author was partially supported by PRONEX #

The object of this paper is to show that the group D ∗ S of S-units of B is generated by elements of small height once S contains an explicit finite set of places of k.. Our

One strategy to answering this question is to compare the χ 2 -statistic of the given table with a large number of randomly selected contingency tables with the same

is the Galols group of the maximal p-extenslon kP/k which is unramlfled outside p and This shows that every central embedding problem E ro for Gk(p) has finite p-I. exponent,

[ChuEF14] Church, Thomas; Ellenberg, Jordan S.; Farb, Benson. Representa- tion stability in cohomology and asymptotics for families of varieties over finite fields. Algebraic

Tensor products of virtual Waldhausen ∞ -categories The derived ∞-category D ≥0 (k) of complexes of vector spaces over a field k with vanishing negative homology inherits a

The theory of log-links and log-shells, both of which are closely related to the lo- cal units of number fields under consideration (Section 5, Section 12), together with the

The theory of log-links and log-shells, which arise from the local units of number fields under consideration (Section 5), together with the Kummer theory that relates