Wyniki wyszukiwania

1

Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces

100%

van Luijk R.

Acta Arithmetica

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2011

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tom 146

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nr 2

153-172

2

Density of rational points on elliptic surfaces

100%

van Luijk R.

Acta Arithmetica

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2012

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tom 156

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nr 2

189-199

3

Explicit Selmer groups for cyclic covers of ℙ¹

63%

Stoll M., van Luijk R.

Acta Arithmetica

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2013

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tom 159

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nr 2

133-148

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.

Ograniczanie wyników

3 Acta Arithmetica

3 van Luijk R.

1 Stoll M.

1 2013

1 2012

1 2011

Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces

Density of rational points on elliptic surfaces

Explicit Selmer groups for cyclic covers of ℙ¹