Grothendieck Duality And Base Change
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Grothendieck Duality And Base Change
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Author : Brian Conrad
language : en
Publisher: Springer
Release Date : 2003-07-01
Grothendieck Duality And Base Change written by Brian Conrad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.
Foundations Of Grothendieck Duality For Diagrams Of Schemes
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Author : Joseph Lipman
language : en
Publisher: Springer
Release Date : 2009-03-07
Foundations Of Grothendieck Duality For Diagrams Of Schemes written by Joseph Lipman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-07 with Mathematics categories.
Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part Two extends the theory to the context of diagrams of schemes.
Foundations Of Grothendieck Duality For Diagrams Of Schemes
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Author : Joseph Lipman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-05
Foundations Of Grothendieck Duality For Diagrams Of Schemes written by Joseph Lipman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-05 with Mathematics categories.
The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings.
Arithmetic Duality Theorems
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Author : J. S. Milne
language : en
Publisher:
Release Date : 1986
Arithmetic Duality Theorems written by J. S. Milne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Galois Cohomology And Class Field Theory
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Author : David Harari
language : en
Publisher: Springer Nature
Release Date : 2020-06-24
Galois Cohomology And Class Field Theory written by David Harari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Vector Bundles On Degenerations Of Elliptic Curves And Yang Baxter Equations
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Author : Igor Burban
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Vector Bundles On Degenerations Of Elliptic Curves And Yang Baxter Equations written by Igor Burban and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
"November 2012, volume 220, number 1035 (third of 4 numbers)."
Motivic Homotopy Theory
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Author : Bjørn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Motivic Homotopy Theory written by Bjørn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work.
Abelian Varieties Theta Functions And The Fourier Transform
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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21
Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Asymptotics For Dissipative Nonlinear Equations
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Author : Nakao Hayashi
language : en
Publisher: Springer
Release Date : 2006-08-23
Asymptotics For Dissipative Nonlinear Equations written by Nakao Hayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-23 with Mathematics categories.
This is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Orthogonal Polynomials And Special Functions
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Author : Francisco Marcellàn
language : en
Publisher: Springer
Release Date : 2006-10-18
Orthogonal Polynomials And Special Functions written by Francisco Marcellàn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-18 with Mathematics categories.
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.