We prove a strong form of the Brumer-Stark Conjecture and, as a consequence, a strong form of Rubin's integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k conta
On a generalization of the rank one Rubin–Stark conjecture
✍ Scribed by Daniel Vallières
- Book ID
- 116673099
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 412 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
Let KÂk be a normal extension of number fields, and / a character on its Galois group G. Stark's conjectures relate the lead term of the Taylor expansion of the Artin L-series L(s, /) at s=0 to the determinant of a matrix whose entries are linear combinations of logs of absolute values of units in K
The work is devoted to the calculation of asymptotic value of the choice number of the complete r-partite graph K m \* r = K m,. ..,m with equal part size m. We obtained the asymptotics in the case ln r = o(ln m). The proof generalizes the classical result of A.L. Rubin for the case r = 2.