Hodge structure on the fundamental group and its application to p-adic integration
| dc.creator | Vologodsky, Vadim | |
| dc.date | 2001-08-16 | |
| dc.date.accessioned | 2026-07-07T04:42:59Z | |
| dc.date.available | 2026-07-07T04:42:59Z | |
| dc.description | We study the unipotent completion $Π^{DR}_{un}(x_0, x_1, X_K)$ of the de Rham fundamental groupoid [De] of a smooth algebraic variety over a local non-archimedean field K of characteristic 0. We show that the vector space $Π^{DR}_{un}(x_0, x_1, X_K)$ possesses a distinguished element. In the other words, given a vector bundle E on $X_K$ together with a unipotent integrable connection, we have {\sf a canonical} isomorphism $E_{x_0}\simeq E_{x_1}$ between the fibers. The latter construction is a generalization of Colmez's p-adic integration (rk E=2) and Coleman's p-adic iterated integrals ($X_K$ is a curve with good reduction). In the second part we prove that, if $X_{K_0}$ is a smooth variety over an unramified extension of $\mathbb{Q}_p$ with good reduction and $r \leq \frac{p-1}{2}$ then there is a canonical isomorphism $Π^{DR}_{r}(x_0, x_1, X_{K_0})\otimes B_{DR} \simeq Π^{et}_{r}(x_0, x_1, X_{\overline K_0}) \otimes B_{DR}$ compatible with the action of Galois group (Here $Π^{DR}_{r}(x_0, x_1, X_{K_0})$ is the level r quotient of $Π^{DR}_{un}(x_0, x_1, X_K)$). In particularly, it implies the Crystalline Conjecture for the fundamental group [Shiho] (for $r \leq \frac{p-1}{2}$) . | |
| dc.description | 44 pages | |
| dc.identifier | https://arxiv.org/abs/math/0108109 | |
| dc.identifier | http://arxiv.org/abs/math/0108109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62026 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Hodge structure on the fundamental group and its application to p-adic integration | |
| dc.type | text |