On the Zeta Function of Forms of Fermat Equations
| dc.creator | Bruenjes, Lars | |
| dc.date | 2003-01-17 | |
| dc.date.accessioned | 2026-07-07T04:54:30Z | |
| dc.date.available | 2026-07-07T04:54:30Z | |
| dc.description | We study ``forms of the Fermat equation'' over an arbitrary field $k$, i.e. homogenous equations of degree $m$ in $n$ unknowns that can be transformed into the Fermat equation $X_1^m+...+X_n^m$ by a suitable linear change of variables over an algebraic closure of $k$. Using the method of Galois descent, we classify all such forms. In the case that $k$ is a finite field of characteristic greater than $m$ that contains the $m$-th roots of unity, we compute the Galois representation on $l$-adic cohomology (and so in particular the zeta function) of the hypersurface associated to an arbitrary form of the Fermat equation. | |
| dc.identifier | https://arxiv.org/abs/math/0301186 | |
| dc.identifier | http://arxiv.org/abs/math/0301186 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66277 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11D41; 11E76; 19F27 | |
| dc.title | On the Zeta Function of Forms of Fermat Equations | |
| dc.type | text |