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On the finiteness of the set of generalized Jacobians with nontrivial torsion points over algebraic number fieldsстатья
- Авторы: Platonov V.P., Zhgoon V.S., Fedorov G.V.
- Журнал: Doklady Mathematics
- Том: 513
- Год издания: 2023
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 66
- Последняя страница: 70
- DOI: 10.1134/S106456242360063X
- Аннотация: For a smooth projective curve C defined over algebraic number field k, we investigate the question of finiteness of the set of generalized Jacobians Jm of a curve C associated with modules m defined over k such that a fixed divisor representing a class of finite order in the Jacobian J of the curve C provides the torsion class in the generalized Jacobian Jm. Various results on the finiteness and infiniteness of the set of generalized Jacobians with the above property are obtained depending on the geometric conditions on the support of m, as well as on the conditions on the field k. These results were applied to the problem of the periodicity of a continuous fraction decomposition constructed in the field of formal power series k((1/x)), for the special elements of the field of functions k(C) of the hyperelliptic curve C:y^2=f(x).
- Добавил в систему: Федоров Глеб Владимирович