Explicit Selmer groups for cyclic covers of ℙ¹

• Autorzy: Michael Stoll , Ronald van Luijk
• Języki publikacji: EN

Abstrakty

EN

For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group $Sel^{ϕ}(J,k)$ is a subgroup of the Galois cohomology group $H¹(Gal(k^{s}/k),J[ϕ])$, defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the `fake Selmer group', whose definition is more amenable to explicit computations. In this paper we define in the same setting the `explicit Selmer group', which is isomorphic to the Selmer group itself and just as amenable to explicit computations as the fake Selmer group. This is useful for describing the associated covering spaces explicitly and may thus help in developing methods for second descents on the Jacobians considered.

Kategorie tematyczne

• 11G10: Abelian varieties of dimension > 1
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14H30: Coverings, fundamental group
• 14H40: Jacobians, Prym varieties
• 14G25: Global ground fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 159
• Numer: 2
• Strony: 133-148

Daty

wydano

2013

Twórcy

autor

Michael Stoll

• Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany

autor

Ronald van Luijk

• Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands

Identyfikatory

DOI

10.4064/aa159-2-4