2008, Approx. 805 p., Hardcover
ISBN: 978-0-387-72491-1
Due: January 2008
About this book
From the reviews of Volume I:
"I am quite happy to keep this volume on my shelf, and I will surely find many more seeds in it that grew so large that by now their origins are hard to recognize."
- Janos Kollar, Bulletin of the AMS
"... a highly valuable and welcome collection for every researcher in the field. … Further generations of researchers in this field, graduate students, mathematical physicists, and mathematical historians will profit a great deal from this collection of selected papers..."
-Werner Kleinert, Zentralblatt MATH
These 30+ articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. While Volume I was very successful, there were papers which were left out, and will now be included here, such as Mumford's paper with Pierre Deligne, The Irreducibility of the space of curves of given genus (1969). Mumford's correspondence with Grothendieck will also be included.
Table of contentsTopology of normal singularities and a criterion for simplicity.- The canononical ring of an algebraic surface.- Some aspects of the problem of moduli.- Two fundamental theorems on deformations of polarized varieties.- A remark on Mordell's conjecture.- Picard groups of moduli problems.- Abelian quotients of the Teichmuller modular group.- Deformations and liftings of finite, commutative group schemes.- Bi-extentions of formal groups.- The irreducibility of the space of curves of given genus.- Varieties defined by quadratric equations, with an appendix by G. Kempf.- A remark on Mahler's compactness theorem.- Introduction to the theory of moduli.- An example of a unirational 3-fold which is not rational.- A remark on the paper of M. Schlessinger.- Matsusaka's big theorem.- The self-intersection formula and the "forumle-clef".- Hilbert's fourteenth problem-the finite generation of subrings such as rings of invariants.- The projectivity of the moduli space of stable curves. I. Preliminaries on "det" and "Div".- An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related nonlinear equation.- The work of C.P. Ramanujam in algebraic geometry.- Some footnotes to the work of C.P. Ramanujam.- Fields medals. IV. An instinct for the key idea.- The spectrum of difference operators and algebraic curves.- Proof of the convexity theorem.- Oscar Zariski: 1899-1986.- Foreward for non-mathematicians.- What can be computed in algebraic geometry.- In memoriam: George R. Kempf 1944-2002.- Boundary points on modular varieties.- Further comments on boundary points.- Abstract theta functions.- Abstract theta functions over local fields.-
Series: Graduate Texts in Mathematics , Preliminary entry 650
2008, Approx. 330 p., Hardcover
ISBN: 978-0-387-72475-1
Due: April 2008
About this textbook
* author has carefully chosen the most important topics within Banach algebra theory
* incorporates recent advances concerning so-called spectral extension properties and the unique uniform norm property
* investigates projective tensor products under all aspects of the book
* exercises are plentiful throughout the text
* class-tested at the University of Heidelberg, Technical University of Munich, and University of Paderborn
This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras, aimed at graduate students with a basic knowledge of functional analysis, topology, complex analysis, measure theory, and group theory. At the core of this text are the chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book is intended for graduate students taking a course on Banach algebras, with various possible specializations, or a Gelfand theory based course in harmonic analysis.
Table of contents
General Theory of Banach Algebras.- Gelfand Theory.- Special Topics.- Regularity and Related Properties.- Spectral Synthesis and Ideal Theory.- Appendix.-
Series: Springer Monographs in Mathematics
2007, XXVI, 792 p., 21 illus., Hardcover
ISBN: 978-3-540-71896-3
Due: September 2007
About this book
The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator.
This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerable attention due to their special role in the theory of linear second-order PDE's with semidefinite characteristic form.
It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry.
It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups.
Table of contents
PART I: Elements of Analysis of Stratified Groups; Stratified Groups and sub-Laplacians.- Abstract Lie Groups and Carnot Groups.- Carnot Groups of Step Two.- Examples of Carnot Groups.- The Fundamental Solution for a sub-Laplacian and Applications.- PART II: Elements of Potential Theory for sub-Laplacians; Abstract Harmonic Spaces.- The L-harmonic Space.- L-subharmonic Functions.- Representation Theorems.- Maximum Principle on Unbounded Domains.- L-capacity, L-polar Sets and Applications.- L-thinness and L-fine Topology .- d-Hausdorff Measure and L-capacity.- PART III: Further Topics on Carnot Groups; Some Remarks on Free Lie Algebras.- More on the Campbell-Hausdorff Formula.- Families of Diffeomorphic sub-Laplacians.- Lifting of Carnot Groups.- Groups of Heisenberg Type.- The Caratheodory-Chow-Rashevsky Theorem.- Taylor Formula on Carnot Groups.
Series: Universitext
Original German edition published by Spektrum
2009, Approx. 400 p., Hardcover
ISBN: 978-0-387-72487-4
Due: July 2009
About this textbook
From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume II the reader can find: the theory of ordered fields (e.g., with reformulation of the fundamental theorem of algebra in terms of ordered fields, with Sylvester's theorem on the number of real roots), Nullstellen-theorems (e.g., with Artin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentals of the theory of quadratic forms, of valuations, local fields and modules. The book also contains some lesser known or nontraditional results; for instance, Tsen's results on solubility of systems of polynomial equations with a sufficiently large number of indeterminates. These two volumes constitute a very good, readable and comprehensive survey of classical algebra and present a valuable contribution to the literature on this subject.
Table of contents
* Formally real fields * Hilbert's 17th problem and Nullstellen- theorems * Orders and quadratic fields * Valuations of fields * Residual degrees and ramification index * Local fields * Witt vectors * Tsen's level of fields * Fundamentals on modules * Wedderburn's theory * Crossed products * Cohomology groups * Brauer group of a local field * Local class field theory * Semisimple representation of finite groups * Schur group of a field