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.
Introduction To Grothendieck Duality Theory
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Author : Allen Altman
language : en
Publisher: Springer
Release Date : 2006-11-15
Introduction To Grothendieck Duality Theory written by Allen Altman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Studies In Duality On Noetherian Formal Schemes And Non Noetherian Ordinary Schemes
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Author : Leovigildo Alonso Tarrío
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Studies In Duality On Noetherian Formal Schemes And Non Noetherian Ordinary Schemes written by Leovigildo Alonso Tarrío 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 1999 with Duality theory (Mathematics). categories.
This volume contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. The first paper presents a self-contained treatment for formal schemes which synthesizes several duality-related topics, such as local duality, formal duality, residue theorems, dualizing complexes, etc. Included is an exposition of properties of torsion sheaves and of limits of coherent sheaves. A second paper extends Greenlees-May duality to complexes on formal schemes. This theorem has important applications to Grothendieck duality. The third paper outlines methods for eliminating the Noetherian hypotheses. A basic role is played by Kiehl's theorem affirming conservation of pseudo-coherence of complexes under proper pseudo-coherent maps. This work gives a detailed introduction to the subject of Grothendieck Duality. The approach is unique in its presentation of a complex series of special cases that build up to the main results.
Introduction To Grothendieck Duality Theory
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Author : Allen Altman
language : en
Publisher: Springer
Release Date : 2014-01-15
Introduction To Grothendieck Duality Theory written by Allen Altman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
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.
Variance And Duality For Cousin Complexes On Formal Schemes
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Author : Joseph Lipman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Variance And Duality For Cousin Complexes On Formal Schemes written by Joseph Lipman 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 2005 with Mathematics categories.
Robert Hartshorne's 1966 book, Residues and Duality, introduced the notion of residual complexes and developed a duality theory (Grothendieck duality) on the category of maps of noetherian schemes. The three articles in this volume constitute a reworking of the main parts of the corresponding chapters in Hartshorne's 1966 book in greater generality using a somewhat different approach. Additionally, the authors' motivation is to help readers gain a better understanding of the relation between local properties of residues and global properties of the dualizing pseudofunctor. The book is suitable for graduate students and researchers working in algebraic geometry.
Etale Cohomology Theory
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Author : Lei Fu
language : en
Publisher: World Scientific
Release Date : 2011
Etale Cohomology Theory written by Lei Fu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
Etale Cohomology Pms 33
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Author : J. S. Milne
language : en
Publisher: Princeton University Press
Release Date : 1980-04-21
Etale Cohomology Pms 33 written by J. S. Milne and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-04-21 with Mathematics categories.
One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Residues And Duality
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Author : Robin Hartshorne
language : en
Publisher: Springer
Release Date : 2006-11-14
Residues And Duality written by Robin Hartshorne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.