On pro-p fundamental groups of marked arithmetic curves
| dc.creator | Schmidt, Alexander | |
| dc.date | 2008-06-11 | |
| dc.date | 2009-01-16 | |
| dc.date.accessioned | 2026-07-07T12:30:08Z | |
| dc.date.available | 2026-07-07T12:30:08Z | |
| dc.description | Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let G_S^T(k)(p)=Gal(k_S^T(p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T. We prove the existence of a finite set of primes S_0, which can be chosen disjoint from any given set M of Dirichlet density zero, such that the cohomology of G_{S\cup S_0}^T(k)(p) coincides with the etale cohomology of the associated marked arithmetic curve. In particular, cd G_{S\cup S_0}^T(k)(p)=2. Furthermore, we can choose S_0 in such a way that k_{S\cup S_0}^T(p) realizes the maximal p-extension k_\p(p) of the local field k_\p for all \p\in S\cup S_0, the cup-product H^1(G_{S\cup S_0}^T(k)(p),\F_p) \otimes H^1(G_{S\cup S_0}^T(k)(p),\F_p) --> H^2(G_{S\cup S_0}^T(k)(p),\F_p) is surjective and the decomposition groups of the primes in S establish a free product inside G_{S\cup S_0}^T(k)(p). This generalizes previous work of the author where similar results were shown in the case T=\emptyset under the restrictive assumption p\nmid Cl(k) and ζ_p\notin k. | |
| dc.description | 28 pages, English translation of arXiv:0806.0772 [math.NT], minor corrections, final version | |
| dc.identifier | https://arxiv.org/abs/0806.1863 | |
| dc.identifier | http://arxiv.org/abs/0806.1863 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216050 | |
| dc.subject | Number Theory | |
| dc.subject | 11R34, 12G10 | |
| dc.title | On pro-p fundamental groups of marked arithmetic curves | |
| dc.type | text |