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1	Auxiliary polynomials and height functions Samuels, Charles Lloyd, 1980- 28 August 2008 (has links) We establish two new results in this dissertation. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number [alpha] under certain assumptions on [alpha]. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number. In particular, we prove the following theorem. [Mathematical equations] / text Polynomials Algebraic spaces
2	Studies in configuration space analysis and applications Kuna, Tobias. January 1999 (has links) Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität. / Includes bibliographical references ((p. 179-187)). Algebraic spaces. Algebraic topology.
3	Auxiliary polynomials and height functions Samuels, Charles Lloyd, January 1900 (has links) Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references. Polynomials. Algebraic spaces.
4	Algebraic structures of signed graphs / Wang, Jue. January 2007 (has links) Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 90-92). Also available in electronic version. Graph theory. Algebraic spaces.
5	Resolutions, bounds, and dimensions for derived categories of varieties Olander, Noah January 2022 (has links) In this thesis we solve three problems about derived categories of algebraic varieties: We prove the conjecture [EL21, Conjecture 4.13] of Elagin and Lunts; we positively answer a question raised by the conjecture [Orl09, Conjecture 10] of Orlov, proving new cases of that conjecture in the process; and we extend Orlov's theorem [Orl97, Theorem 2.2] from smooth projective varieties to smooth proper algebraic spaces. These results go toward answering the questions: How rigid is the (triangulated) derived category of coherent sheaves on an algebraic variety, and how much information does it possess about the variety? Our techniques are general and work for algebraic spaces just as well as they do for projective varieties. Mathematics Algebraic spaces Sheaf theory
6	Projective anabelian curves in positive characteristic and descent theory for log-étale covers Stix, Jakob. January 2002 (has links) Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2002. / Includes bibliographical references.
7	Topology of singular spaces and constructible sheaves / Schürmann, Jörg. January 2003 (has links) Univ., FB Mathematik, Habil.-Schr., 2001--Hamburg, 2001.
8	Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces Tshilombo, Mukinayi Hermenegilde 08 1900 (has links) This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics) Constant dimension Locally Euclidean Frolicher spaces Symplectic structure Symplectic geometry Symplectic quotient or reduced space Exterior algebra Ringed Frolicher space Smooth Gelfand representation Sheaf cohomology Alexander-Spanier cohomology Singular cohomology Cech cohomology and de Rham cohomology Vector fields and mechanics 514.224 Homology theory Symplectic manifolds Topological spaces Sheaf theory Geometry, Differential Hamiltonian graph theory Algebraic spaces
9	Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces Tshilombo, Mukinayi Hermenegilde 08 1900 (has links) This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics) Constant dimension Locally Euclidean Frolicher spaces Symplectic structure Symplectic geometry Symplectic quotient or reduced space Exterior algebra Ringed Frolicher space Smooth Gelfand representation Sheaf cohomology Alexander-Spanier cohomology Singular cohomology Cech cohomology and de Rham cohomology Vector fields and mechanics 514.224 Homology theory Symplectic manifolds Topological spaces Sheaf theory Geometry, Differential Hamiltonian graph theory Algebraic spaces

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