Massey Products and Ideal Class Groups
| dc.creator | Sharifi, Romyar | |
| dc.date | 2003-08-18 | |
| dc.date | 2007-03-17 | |
| dc.date.accessioned | 2026-07-07T07:52:12Z | |
| dc.date.available | 2026-07-07T07:52:12Z | |
| dc.description | We consider certain Massey products in the cohomology of a Galois extension of fields with coefficients in p-power roots of unity. We prove formulas for these products both in general and in the special case that the Galois extension in question is the maximal extension of a number field unramified outside a set of primes S including those above p and any archimedean places. We then consider those Z_p-Kummer extensions L of the maximal p-cyclotomic extension K of a number field that are unramified outside S. We show that Massey products describe the structure of a certain "decomposition-free" quotient of a graded piece of the maximal unramified abelian pro-p extension of L in which all primes above those in S split completely, with the grading arising from the augmentation filtration on the group ring of the Galois group of L/K. We explicitly describe examples of the maximal unramified abelian pro-p extensions of unramified outside p Kummer extensions of the cyclotomic field of all p-power roots of unity, for irregular primes p. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308165 | |
| dc.identifier | http://arxiv.org/abs/math/0308165 | |
| dc.identifier | J. reine angew. Math. 603 (2007) 1-33 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125795 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23 (Primary) 11R34, 11R29, 11R20, 12G05 (Secondary) | |
| dc.title | Massey Products and Ideal Class Groups | |
| dc.type | text |