S Modules In The Category Of Schemes

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S Modules In The Category Of Schemes

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Author : Po Hu
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

S Modules In The Category Of Schemes written by Po Hu 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 2003 with Mathematics categories.

Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.

The Geometry Of Schemes

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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

The Geometry Of Schemes written by David Eisenbud 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 2006-04-06 with Mathematics categories.

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Drinfeld Modules Modular Schemes And Applications

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Author : M Van Der Put
language : en
Publisher: World Scientific
Release Date : 1997-08-27

Drinfeld Modules Modular Schemes And Applications written by M Van Der Put and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-27 with Mathematics categories.

In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.

Algebraic Geometry Ii Cohomology Of Schemes

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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2023-11-22

Algebraic Geometry Ii Cohomology Of Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-22 with Mathematics categories.

This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.

Drinfeld Moduli Schemes And Automorphic Forms

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Author : Yuval Z Flicker
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04

Drinfeld Moduli Schemes And Automorphic Forms written by Yuval Z Flicker 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 2013-01-04 with Mathematics categories.

Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.

S Modules In The Category Of Schemes

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Author : Po Hu
language : en
Publisher:
Release Date : 2014-09-11

S Modules In The Category Of Schemes written by Po Hu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Categories categories.

Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.

Algebraic Geometry I Schemes

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Author : Ulrich Görtz
language : en
Publisher: Springer Nature
Release Date : 2020-07-27

Algebraic Geometry I Schemes written by Ulrich Görtz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-27 with Mathematics categories.

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Heegner Modules And Elliptic Curves

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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Heegner Modules And Elliptic Curves written by 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 2004 with Algebraic fields categories.

Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes

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Author : Leonid Positselski
language : en
Publisher: Springer Nature
Release Date : 2023-09-14

Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes written by Leonid Positselski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.

Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.

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.