Introduction to Grothendieck Duality Theory PDF Download

Author: Allen Altman
Publisher: Springer
ISBN: 3540363092
Category : Mathematics
Languages : en
Pages : 188

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Author: Brian Conrad
Publisher: Springer
ISBN: 354040015X
Category : Mathematics
Languages : en
Pages : 302

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Book Description
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.

Author: Joseph Lipman
Publisher: Springer
ISBN: 3540854207
Category : Mathematics
Languages : en
Pages : 471

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Book Description
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.

Author: Allen Altman
Publisher: Springer
ISBN: 9783662165522
Category :
Languages : en
Pages : 192

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Author: J. S. Milne
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440

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Book Description
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.

Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273

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Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author: Lou Van den Dries
Publisher: Cambridge University Press
ISBN: 0521598389
Category : Mathematics
Languages : en
Pages : 196

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Book Description
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.

Author: Richard Hartshorne
Publisher:
ISBN: 9780387036038
Category :
Languages : en
Pages :

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Author: M. P. Brodmann
Publisher: Cambridge University Press
ISBN: 0521513634
Category : Mathematics
Languages : en
Pages : 514

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Book Description
On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.

Author: Barbara Fantechi
Publisher: American Mathematical Soc.
ISBN: 0821842455
Category : Mathematics
Languages : en
Pages : 354

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Book Description
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.