Wyniki wyszukiwania

1

Implementing 2-descent for Jacobians of hyperelliptic curves

100%

Stoll M.

Acta Arithmetica

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2001

|

tom 98

|

nr 3

245-277

2

On the height constant for curves of genus two

100%

Stoll M.

Acta Arithmetica

|

1999

|

tom 90

|

nr 2

183-201

3

On the number of rational squares at fixed distance from a fifth power

100%

Stoll M.

Acta Arithmetica

|

2006

|

tom 125

|

nr 1

79-88

4

On the height constant for curves of genus two, II

100%

Stoll M.

Acta Arithmetica

|

2002

|

tom 104

|

nr 2

165-182

5

Explicit Selmer groups for cyclic covers of ℙ¹

64%

Stoll M., van Luijk R.

Acta Arithmetica

|

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.

6

On the Diophantine equation $X^2 - (2^{2m}+1)Y^4 = -2^{2m}$

51%

Stoll M., Walsh P., Yuan P.

Acta Arithmetica

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2009

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tom 139

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nr 1

57-63

Ograniczanie wyników

6 Acta Arithmetica

6 Stoll M.

1 Walsh P.

1 Yuan P.

1 van Luijk R.

1 2013

1 2009

1 2006

1 2002

1 2001

1 1999

Implementing 2-descent for Jacobians of hyperelliptic curves

On the height constant for curves of genus two

On the number of rational squares at fixed distance from a fifth power

On the height constant for curves of genus two, II

Explicit Selmer groups for cyclic covers of ℙ¹

On the Diophantine equation $X^2 - (2^{2m}+1)Y^4 = -2^{2m}$