Rank One Solvable p-adic Differential Equation and Finite Abelian Characters via Lubin-Tate groups
| dc.creator | Pulita, Andrea | |
| dc.date | 2006-12-27 | |
| dc.date | 2006-12-28 | |
| dc.date.accessioned | 2026-07-07T07:37:21Z | |
| dc.date.available | 2026-07-07T07:37:21Z | |
| dc.description | We introduce a new class of exponentials of Artin-Hasse type, called $\boldsymbolπ$-exponentials. These exponentials depends on the choice of a generator $\boldsymbolπ$ of the Tate module of a Lubin-Tate group $\mathfrak{G}$ over $\mathbb{Z}_p$. They arise naturally as solutions of solvable differential modules over the Robba ring. If $\mathfrak{G}$ is isomorphic to $\hat{\mathbb{G}}_m$ over $\mathbb{Z}_p$, we develop methods to test their over-convergence, and get in this way a stronger version of the Frobenius structure theorem for differential equations. We define a natural transformation of the Artin-Schreier complex into the Kummer complex. This provides an explicit generator of the Kummer unramified extension of $\mathcal{E}^†_{K_{\infty}}$, whose residue field is a given Artin-Schreier extension of k((t)), where k is the residue field of K. We then compute explicitely the group, under tensor product, of isomorphism classes of rank one solvable differential equations. Moreover, we get a canonical way to compute the rank one $ϕ$-module over $\mathcal{E}^†_{K_{\infty}}$ attached to a rank one representation of $Gal(k((t))^{sep}/k((t)))$, defined by an Artin-Schreier character. | |
| dc.description | 53 Pages, this is not the published version. To appear in Math.Annalen. On line version avaiable at the following addres: http://springerlink.metapress.com/content/1432-1807/?sortorder=asc&sw=rank+one | |
| dc.identifier | https://arxiv.org/abs/math/0612725 | |
| dc.identifier | http://arxiv.org/abs/math/0612725 | |
| dc.identifier | doi:10.1007/s00208-006-0040-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120748 | |
| dc.subject | Number Theory | |
| dc.subject | 12h25; 11S15; 11S20; 14F30 | |
| dc.title | Rank One Solvable p-adic Differential Equation and Finite Abelian Characters via Lubin-Tate groups | |
| dc.type | text |