Periods and algebraic deRham cohomology
| dc.creator | Friedrich, Benjamin | |
| dc.date | 2005-06-07 | |
| dc.date.accessioned | 2026-07-07T06:26:46Z | |
| dc.date.available | 2026-07-07T06:26:46Z | |
| dc.description | It is known that the algebraic \deRham cohomology group $\hDR{i}(X_0/\Q)$ of a nonsingular variety $X_0/\Q$ has the same rank as the rational singular cohomology group $\h^i\sing(\Xh;\Q)$ of the complex manifold $\Xh$ associated to the base change $X_0\times_{\Q}\C$. However, we do not have a natural isomorphism $\hDR{i}(X_0/\Q)\iso\h^i\sing(\Xh;\Q)$. Any choice of such an isomorphism produces certain integrals, so called periods, which reveal valuable information about $X_0$. The aim of this thesis is to explain these classical facts in detail. Based on an approach of Kontsevich, different definitions of a period are compared and their properties discussed. Finally, the theory is applied to some examples. These examples include a representation of $ζ(2)$ as a period and a variation of mixed Hodge structures used by Goncharov. | |
| dc.description | 103 pages, 12 figures, diploma thesis | |
| dc.identifier | https://arxiv.org/abs/math/0506113 | |
| dc.identifier | http://arxiv.org/abs/math/0506113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97209 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F40 | |
| dc.title | Periods and algebraic deRham cohomology | |
| dc.type | text |