Diss.--Universität Erlangen-Nürnberg, Erlangen. / Vita. Bibliography: p. 77-78.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004. / Includes bibliographical references (p. 109-110).

For any ring R (associative with 1) we associate a space X of prime torsion theories endowed with Golan's SBO-topology. A separated presheaf L(-,M) on X is then constructed for any right R-module M$ sb{ rm R}$, and a sufficient condition on M is given such that L(-,M) is actually a sheaf. The sheaf space rm E { buildrel{ rm p} over longrightarrow} X) etermined by L(-,M) represents M in the following sense: M is isomorphic to the module of continuous global sections of p. These results are applied to the right R-module R$ sb{ rm R}$ and it is seen that semiprime rings satisfy the required condition for L(-,R) to be a sheaf. Among semiprime rings two classes are singled out, fully symmetric semiprime and right noetherian semiprime rings; these two kinds of rings have the desirable property of yielding "nice" stalks for the above sheaf.

One of the earlier achievements of twistor theory was the description of free zero rest mass fields on complexified Minkowski space in terms of holomorphic functions on twistor space. Interactions between these fields are given by certain spacetime integrals (represented by Feynmann diagrams), and some of these integrals have been translated into contour integrals in products of twistor spaces (represented by twistor diagrams). The principal advantage of the twistor diagram formalism is that it is necessarily finite. The main purpose of this thesis is to explore the uses of two mathematical techniques in twistor diagrams. The first is the "blowing up" process familiar to algebraic geometers. It arises naturally in the translation from the massless scalar ϕ⁴(vertex to the corresponding twistor diagram (called the "box" diagram). A detailed study of this translation reveals that there are three contours over which the box diagram can be integrated, one for each of the channels in the ϕ⁴ interaction. The second technique is sheaf cohomology theory, vhich vas introduced to make rigorous the twistor description of zero rest mass fields by replacing twistor functions by elements of sheaf cohomology groups. We show how to interpret fragments of twistor diagrams - which normally represent twistor functions - as these sheaf cohomology elements. Chapter 1 introduces, briefly, the basic ideas of twistor geometry, the twistor description of fields, and twistor diagrams. In chapter 2 we demonstrate the existence of contours for part of the Möller scattering diagram using singular homology theory, while chapter 3 gives the details of the translation to the box diagram (already referred to) and compares it with the scalar product diagram. The last two chapters (4 and 5) deal with the sheaf cohomology of tree diagrams and the scalar product diagram respectively.

Diss. (sammanfattning) Uppsala : Univ., 2003. / Härtill 3 uppsatser.

Please read the abstract in the section front of this document. / Thesis (PhD)--University of Pretoria, 2010. / Mathematics and Applied Mathematics / unrestricted

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.

No description available.