Eriksen / Laudal / Siqveland Noncommutative Deformation Theory

1. Auflage 2017
ISBN: 978-1-4987-9602-6
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 258 Seiten

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Deformation theory is used as a tool for studying the structure of moduli schemes in geometry by many mathematicians and physicists. Mainly, the structure of the obstruction groups and their vanishing is used for smoothness properties, but there is a need to find the structure of the singularities in moduli spaces as well. This can only be achieved by constructing the singularities, and this can be done by the deformation theory studied in this book, in particular in the study of liftings by generalized matric Massey products.

Autoren/Hrsg.

Eriksen, Eivind

Laudal, Olav Arnfinn

Siqveland, Arvid

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

1. Introduction. 2. Preliminaries. 2.1 Notation and terminology. 2.2 Commutative deformation theory. 2.3 Noncommutative algebra. 2.4 Simple modules. 3. Noncommutative Deformation Theory. 3.1 Noncommutative Deformations. 3.2 Obstruction Theory. 3.3 The Semi-local Formal Moduli and Generalized Matric Massey Products 3.4 The Generalized Burnside’s Theorem. 3.5 Application to Beilinson theory. 3.6 Deformation due to Diagrams. 4. Noncommutative Schemes. 4.1 Review of Existing theory. 4.2 The Scheme of Simple Modules Simp-infty. 4.3 Noncommutative Schemes and the Serre Theorem. 4.4 Noncommutative Varieties. 4.5 Phase spaces Ph(A)

Über Autor(innen)

Olav Arnfinn Laudal is Professor Emeritus at University of Oslo. He has had a long life in algebraic geometry, and is well known for his work in deformation theory. He has had a lot of students, including the co-authors of this book. More can be found on his home-page (http://folk.uio.no/arnfinnl/). Eivind Eriksen is one of Laudal’s last PhD students, working with deformation theory, more on http://home.bi.no/a0710194/. Associate professor at BI Norwegian Business School