Search for dissertations about: "Abelian Varieties"

Found 4 swedish dissertations containing the words Abelian Varieties.

  2. 1. Computing abelian varieties over finite fields

    Author : Stefano Marseglia; Jonas Bergström; Christophe Ritzenthaler; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; abelian varieties; finite fields; period matrices; ideal classes; orders; number fields; integral matrices; Mathematics; matematik;

    Abstract : In this thesis we address the problem of developing effective algorithms to compute isomorphism classes of polarized abelian varieties over a finite field and of fractional ideals of an order in a finite product of number fields.There are well-known methods to efficiently compute the classes of invertible ideals of an order in a number field, but not much has previously been known about non-invertible ideals. READ MORE

  4. 2. Isomorphism classes of abelian varieties over finite fields

    Author : Stefano Marseglia; Jonas Bergström; Lars Halle; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Algebraic Geometry; Abelian Varieties; Finite Fields; Ideal Class Group; Ideal Class Monoid;

    Abstract : Deligne and Howe described polarized abelian varieties over finite fields in terms of finitely generated free Z-modules satisfying a list of easy to state axioms. In this thesis we address the problem of developing an effective algorithm to compute isomorphism classes of (principally) polarized abelian varieties over a finite field, together with their automorphism groups. READ MORE

  5. 3. Ekedahl Invariants, Veronese Modules and Linear Recurrence Varieties

    Author : Ivan Martino; Anders Björner; Volkmar Welker; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Ekedahl Invariants; Noether Problem; Bogomolov Multiplier; Cyclic quotient singularities; Veronese Modules; Pile simplicial complex; Semigroup Rings; Betti Numbers; Mathematics; matematik;

    Abstract : The title of this thesis refers to the three parts of which it is composed.The first part concerns the Ekedahl Invariants, new geometric invariants for finite groups introduced in 2009 by Torsten Ekedahl. READ MORE

  6. 4. Destackification and Motivic Classes of Stacks

    Author : Daniel Bergh; David Rydh; Dan Edidin; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Algebraic geometry; Algebraic stacks; Destackification; Grothendieck ring; Motive; Torus; Classifying stack; Mathematics; matematik;

    Abstract : This thesis consists of three articles treating topics in the theory of algebraic stacks. The first two papers deal with motivic invariants. In the first, we show that the class of the classifying stack BPGLn is the inverse of the class of PGLn in the Grothendieck ring of stacks for n ≤ 3. READ MORE