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@article{840938, author = {Greither, Cornelius and Kučera, Radan}, article_location = {Berlín}, article_number = {1}, keywords = {Stark units; regulators; Gross conjecture on tori}, language = {eng}, issn = {0075-4102}, journal = {Journal für die reine und angewandte Mathematik}, title = {The Minus Conjecture revisited}, url = {http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.053}, volume = {632}, year = {2009} }
TY - JOUR ID - 840938 AU - Greither, Cornelius - Kučera, Radan PY - 2009 TI - The Minus Conjecture revisited JF - Journal für die reine und angewandte Mathematik VL - 632 IS - 1 SP - 127-142 EP - 127-142 PB - Walter de Gruyter & co SN - 00754102 KW - Stark units KW - regulators KW - Gross conjecture on tori UR - http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.053 N2 - In an earlier paper we proved some results concerning Gross's conjecture on tori. This conjecture, which we call the Minus Conjecture, is closely related to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however Burns' conjecture does not directly imply the Minus Conjecture. The result proved in the earlier paper was concerned with imaginary absolutely abelian extensions K/Q of the form K=FK+, with F imaginary quadratic and K+/Q being tame, l-elementary and ramified at most at two primes. In the present paper we complement these results by proving the Minus Conjecture for extensions K/Q as above but without any restriction on the number s of ramified primes. The price we have to pay for this generality is that our proof only works if the odd prime l>=3(s+1) and l does not divide hF. ER -
GREITHER, Cornelius a Radan KUČERA. The Minus Conjecture revisited. \textit{Journal für die reine und angewandte Mathematik}. Berlín: Walter de Gruyter \&{} co, 2009, roč.~632, č.~1, s.~127-142. ISSN~0075-4102.
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