On Galois groups of unramified pro-p extensions
| dc.creator | Sharifi, Romyar T. | |
| dc.date | 2008-01-09 | |
| dc.date | 2008-05-21 | |
| dc.date.accessioned | 2026-07-07T09:53:23Z | |
| dc.date.available | 2026-07-07T09:53:23Z | |
| dc.description | Let p be an odd prime satisfying Vandiver's conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z_p-extensions of the pth cyclotomic field and the Galois group G of the unramified pro-p extension of the cyclotomic field of all p-power roots of unity. We give a lower bound for the height of the annihilator of X as an Iwasawa module. Under some mild assumptions on Bernoulli numbers, we provide a necessary and sufficient condition for G to be abelian. The bound and the condition in the two results are given in terms of the special values of a cup product pairing on cyclotomic p-units. We obtain, in particular, that for p less than 1000, Greenberg's conjecture on the pseudo-nullity of X holds and G is in fact abelian. | |
| dc.description | 14 pages: substantial revisions, final version, to appear in Math. Ann | |
| dc.identifier | https://arxiv.org/abs/0801.1360 | |
| dc.identifier | http://arxiv.org/abs/0801.1360 | |
| dc.identifier | Math. Ann. 342 (2008) 297-308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165933 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23; 11R32; 11R18 | |
| dc.title | On Galois groups of unramified pro-p extensions | |
| dc.type | text |