Search for dissertations about: "ideal classes"
Showing result 1 - 5 of 30 swedish dissertations containing the words ideal classes.
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1. Isomorphism classes of abelian varieties over finite fields
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
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2. Computing abelian varieties over finite fields
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
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3. Integral Closure and Related Operations on Monomial Ideals
Abstract : The motivation for this thesis starts with the theory of Hilbert coefficients. It is a well known fact that given an ideal I the integral closure Ī can be defined as the largest ideal with the same multiplicity as I. For monomial ideals there is an alternative definition. READ MORE
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4. Around power ideals : From Fröberg's conjecture to zonotopal algebra
Abstract : In this thesis we study power algebras, which are quotient of polynomial rings by power ideals. We will study Hilbert series of such ideals and their other properties. We consider two important special cases, namely, zonotopal ideals and generic ideals. Such ideals have a lot combinatorial properties. READ MORE
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5. Quaternion Orders and Ternary Quadratic Forms Orders of Class Number One and Representations of Algebraic Integers by Quadratic Forms
Abstract : Let R be the ring of integers in a totally real quadratic field K. The purpose of the thesis is to study totally definite quaternion R-orders and representations of elements in R by totally positive definite integral ternary quadratic forms. The thesis consists of three papers. READ MORE