The 2-primary class group of certain hyperelliptic curves
| dc.creator | Cornelissen, Gunther | |
| dc.date | 1999-08-31 | |
| dc.date | 1999-09-01 | |
| dc.date.accessioned | 2026-07-07T05:30:35Z | |
| dc.date.available | 2026-07-07T05:30:35Z | |
| dc.description | Let G be the separable Galois group of a finite field F of characteristic p, and X/F an imaginary hyperelliptic curve such that G acts transitively on its set W(X) of Weierstrass points. The existence of a G-invariant 2-torsion point on the Jacobian J(X) of X depends only on the parity of |W(X)|, but for large enough |F|, there exist two such curves X and X' with |W(X)|=|W(X')|, such that J(X) has (and J(X') does not have) a G-invariant 4-torsion point. The problem is equivalent to a study of the 2-,4- and 8-rank of the class number of the maximal order in the function field of such curves, and is investigated via the 2-primary class field tower. Contrary to the case of number fields, the ambiguous class depends on the discriminant, and a governing field for the 8-rank of such function fields is not known. | |
| dc.description | 10 pages, LaTeX, uses `a4' | |
| dc.identifier | https://arxiv.org/abs/math/9908175 | |
| dc.identifier | http://arxiv.org/abs/math/9908175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79039 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11R29, 14H40 | |
| dc.title | The 2-primary class group of certain hyperelliptic curves | |
| dc.type | text |