About the choice of a basis in Kedlaya's algorithm
| dc.creator | Bogaart, Theo van den | |
| dc.date | 2008-09-07 | |
| dc.date.accessioned | 2026-07-07T10:01:20Z | |
| dc.date.available | 2026-07-07T10:01:20Z | |
| dc.description | Kedlaya's algorithm (Kedlaya, J. Ramanujan Math. Soc 16, 2001) can be used to count the points of arbitrary hyperelliptic curves over finite fields of characteristic p, where p is an odd prime. The algorithm uses the cohomology of a p-adic lift of the curve. The Frobenius morphism of the curve induces an automorphism of this cohomological space. The key step of the algorithm is to determine this automorphism with a sufficiently high p-adic precision: it is given in the form of a matrix with respect to a certain basis. Edixhoven has found a basis that has the property that the coefficients of the matrix are p-adically integral. This allows a smaller required precision, because a (semi-linear) power of this matrix must be computed up to some given precision. This text describes Edixhoven's basis and provides a proof of the fact that the basis is suitable. | |
| dc.description | This is a (fully independent) chapter of the author's PhD thesis | |
| dc.identifier | https://arxiv.org/abs/0809.1243 | |
| dc.identifier | http://arxiv.org/abs/0809.1243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168600 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | About the choice of a basis in Kedlaya's algorithm | |
| dc.type | text |