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Michael Stoll

  1. Unfaking the fake Selmer group.

    Чт, 08/18/2011 - 15:01 — SomNambul
    Authors: Michael Stoll, Ronald van Luijk
    Subjects: Algebraic Geometry
    Abstract

    For any abelian variety J over a global field k and an isogeny phi: J -> J,
    the Selmer group Sel^phi(J,k) is a subgroup of the Galois cohomology group
    H^1(Gal(k^s/k),J[phi]), defined in terms of local data. When J is the Jacobian
    of a cyclic cover of P^1, the Selmer group has a quotient by a subgroup of
    order at most 2 that is isomorphic to the `fake Selmer group', whose definition
    is more amenable to explicit computations.

  2. How to Solve a Diophantine Equation.

    Ср, 02/24/2010 - 16:01 — SomNambul
    Authors: Michael Stoll
    Subjects: Number Theory
    Abstract

    These notes represent an extended version of a talk I gave for the
    participants of the IMO 2009 and other interested people. We introduce
    diophantine equations and show evidence that it can be hard to solve them. Then
    we demonstrate how one can solve a specific equation related to numbers
    occurring several times in Pascal's Triangle with state-of-the-art methods.

  3. On a problem of Hajdu and Tengely.

    Втр, 12/15/2009 - 16:01 — SomNambul
    Authors: Michael Stoll, Samir Siksek
    Subjects: Number Theory
    Abstract

    We answer a question asked by Hajdu and Tengely: The only arithmetic
    progression in coprime integers of the form (a^2, b^2, c^2, d^5) is (1, 1, 1,
    1).

  4. Reduction theory of point clusters in projective space.

    Ср, 09/16/2009 - 13:15 — SomNambul
    Authors: Michael Stoll
    Subjects: Number Theory
    Abstract

    In this paper, we generalise results obtained earlier by John Cremona and the
    author on the reduction theory of binary forms, which describe positive
    zero-cycles in P^1, to positive zero-cycles (or point clusters) in projective
    spaces of arbitrary dimension. This should have applications to more general
    projective varieties in P^n, by associating a suitable positive zero-cycle to
    them in an PGL(n+1)-invariant way. We discuss this in the case of (smooth)
    plane curves.

  5. Reduction theory of point clusters in projective space.

    Ср, 09/16/2009 - 13:15 — SomNambul
    Authors: Michael Stoll
    Subjects: Number Theory
    Abstract

    In this paper, we generalise results obtained earlier by John Cremona and the
    author on the reduction theory of binary forms, which describe positive
    zero-cycles in P^1, to positive zero-cycles (or point clusters) in projective
    spaces of arbitrary dimension. This should have applications to more general
    projective varieties in P^n, by associating a suitable positive zero-cycle to
    them in an PGL(n+1)-invariant way. We discuss this in the case of (smooth)
    plane curves.

Math-arch

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