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Andreas Maurischat

  1. On the finite generation of additive group invariants in positive characteristic.

    Ср, 01/20/2010 - 16:01 — SomNambul
    Authors: Andreas Maurischat, Emilie Dufresne
    Subjects: Commutative Algebra
    Abstract

    Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest
    counterexamples to Hilbert's fourteenth problem as rings of invariants of
    algebraic groups. Each is of an action of the additive group on a finite
    dimensional vector space over a field of characteristic zero, and thus, each is
    the kernel of a locally nilpotent derivation. In positive characteristic,
    additive group actions correspond to locally finite iterative higher
    derivations.

  2. Galois theory for iterative connections and nonreduced Galois groups.

    Чт, 08/27/2009 - 13:23 — SomNambul
    Authors: Andreas Maurischat
    Subjects: Rings and Algebras
    Abstract

    This article presents a theory of modules with iterative connection. This
    theory is a generalisation of the theory of modules with connection in
    characteristic zero to modules over rings of arbitrary characteristic. We show
    that these modules with iterative connection (and also the modules with
    integrable iterative connection) form a Tannakian category, assuming some nice
    properties for the underlying ring, and we show how this generalises to modules
    over schemes. We also relate these notions to stratifications on modules, as
    introduced by A.

  3. Infinitesimal group schemes as iterative differential Galois groups.

    Чт, 08/27/2009 - 13:23 — SomNambul
    Authors: Andreas Maurischat
    Subjects: Rings and Algebras
    Abstract

    This article is concerned with Galois theory for iterative differential
    fields (ID-fields) in positive characteristic. More precisely, we consider
    purely inseparable Picard-Vessiot extensions, because these are the ones having
    an infinitesimal group scheme as iterative differential Galois group. In this
    article we prove a necessary and sufficient condition to decide whether an
    infinitesimal group scheme occurs as Galois group scheme of a Picard-Vessiot
    extension over a given ID-field or not. In particular, this solves the inverse
    ID-Galois problem for infinitesimal group schemes.

  4. Infinitesimal group schemes as iterative differential Galois groups.

    Чт, 08/27/2009 - 13:23 — SomNambul
    Authors: Andreas Maurischat
    Subjects: Rings and Algebras
    Abstract

    This article is concerned with Galois theory for iterative differential
    fields (ID-fields) in positive characteristic. More precisely, we consider
    purely inseparable Picard-Vessiot extensions, because these are the ones having
    an infinitesimal group scheme as iterative differential Galois group. In this
    article we prove a necessary and sufficient condition to decide whether an
    infinitesimal group scheme occurs as Galois group scheme of a Picard-Vessiot
    extension over a given ID-field or not. In particular, this solves the inverse
    ID-Galois problem for infinitesimal group schemes.

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