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Author: Paul Feit
Publisher:
ISBN:
Category :
Languages : en
Pages : 107
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Book Description
Author: Paul Feit
Publisher:
ISBN:
Category :
Languages : en
Pages : 107
Get Book Here
Book Description
Author: Paul Feit
Publisher: American Mathematical Soc.
ISBN: 0821825461
Category : Categories
Languages : en
Pages : 121
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Book Description
This paper offers a systematic approach to all mathematical theories with local/global behavior. To build objects with local and global aspects, on begins with a category of [script]C of allowed local structures, and somehow derives a category [script]C[superscript]gl of things which are 'locally' in [script]C. Some global objects, such as manifolds or schemes, can be represented as a sheaf of algebras on a topological base space; others, like algebraic spaces, are more technical. These theories share common structure--certain theorems on inverse limits, descent, and dependence on special class of morphism appear in all cases. Yet, classical proofs for universal properties proceed by case-by-case study. Separate examples require distinct arguments.
Author: Paul Feit
Publisher: American Mathematical Soc.
ISBN: 9780821862087
Category : Mathematics
Languages : en
Pages : 126
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Book Description
Requiring only familiarity with the terminology of categories, this book will interest algebraic geometers and students studying schemes for the first time. Feit translates the geometric intuition of local structure into a purely categorical format, filling a gap at the foundations of algebraic geometry. The main result is that, given an initial category ${\cal C $ of ''local'' objects and morphisms, there is a canonical enlargement of ${\cal C $ to a category ${\cal C {gl $ which contains all ''global'' objects whose local structure derives from ${\cal C $ and which is functorially equivalent to the traditional notion of ''global objects''. Using this approach, Feit unifies definitions for numerous technical objects of algebraic geometry, including schemes, Tate's rigid analytic spaces, and algebraic spaces.
Author: Igor Frenkel
Publisher: American Mathematical Soc.
ISBN: 0821825550
Category : Mathematics
Languages : en
Pages : 79
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Book Description
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.
Author: Maria del Rosario Gonzalez-Dorrego
Publisher: American Mathematical Soc.
ISBN: 0821825747
Category : Mathematics
Languages : en
Pages : 114
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Book Description
The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.
Author: John Roe
Publisher: American Mathematical Soc.
ISBN: 0821825593
Category : Mathematics
Languages : en
Pages : 106
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Book Description
"July 1993, volume 104, number 497 (fourth of 6 numbers)."
Author: Shirō Gotō
Publisher: American Mathematical Soc.
ISBN: 0821825844
Category : Mathematics
Languages : en
Pages : 149
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Book Description
At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).
Author: Kevin W. J. Kadell
Publisher: American Mathematical Soc.
ISBN: 0821825526
Category : Mathematics
Languages : en
Pages : 93
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Book Description
Macdonald and Morris gave a series of constant term [italic]q-conjectures associated with root systems. Selberg evaluated a multivariable beta-type integral which plays an important role in the theory of constant term identities associated with root systems. K. Aomoto recently gave a simple and elegant proof of a generalization of Selberg's integral. Kadell extended this proof to treat Askey's conjectured [italic]q-Selberg integral, which was proved independently by Habsieger. We use a constant term formulation of Aomoto's argument to treat the [italic]q-Macdonald-Morris conjecture for the root system [italic capitals]BC[subscript italic]n. We show how to obtain the required functional equations using only the q-transportation theory for [italic capitals]BC[subscript italic]n.
Author: Stanley O. Kochman
Publisher: American Mathematical Soc.
ISBN: 0821825585
Category : Mathematics
Languages : en
Pages : 105
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Book Description
This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.
Author: Roger D. Nussbaum
Publisher: American Mathematical Soc.
ISBN: 0821824546
Category : Mathematics
Languages : en
Pages : 148
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Book Description
