The Grothendieck Festschrift Volume Iii
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| Author | : Pierre Cartier |
| Publisher | : Springer |
| Total Pages | : 499 |
| Release | : 2007-10-23 |
| Genre | : Mathematics |
| ISBN | : 0817645764 |
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
| Author | : Pierre Cartier |
| Publisher | : |
| Total Pages | : 518 |
| Release | : 1990 |
| Genre | : Geometry, Algebraic |
| ISBN | : |
| Author | : Pierre Cartier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 514 |
| Release | : 2009-05-21 |
| Genre | : Mathematics |
| ISBN | : 0817645748 |
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.
| Author | : Dennis Gaitsgory |
| Publisher | : American Mathematical Society |
| Total Pages | : 436 |
| Release | : 2020-10-07 |
| Genre | : Mathematics |
| ISBN | : 1470452855 |
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on such. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained. This volume consists of two parts. The first part introduces the notion of ind-scheme and extends the theory of ind-coherent sheaves to inf-schemes, obtaining the theory of D-modules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of ind-coherent sheaves. This equivalence gives a vast generalization of the equivalence between Lie algebras and formal moduli problems. This theory is applied to study natural filtrations in formal derived geometry generalizing the Hodge filtration.
| Author | : Nitya Kitchloo, Mona Merling |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 208 |
| Release | : 2018-05-29 |
| Genre | : Mathematics |
| ISBN | : 1470437740 |
This volume contains the proceedings of the Second Mid-Atlantic Topology Conference, held from March 12–13, 2016, at Johns Hopkins University in Baltimore, Maryland. The focus of the conference, and subsequent papers, was on applications of innovative methods from homotopy theory in category theory, algebraic geometry, and related areas, emphasizing the work of younger researchers in these fields.
| Author | : Eric Friedlander |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1148 |
| Release | : 2005-07-18 |
| Genre | : Mathematics |
| ISBN | : 354023019X |
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
| Author | : Mark Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 366205650X |
This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
| Author | : Ulrich Görtz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 622 |
| Release | : 2010-08-06 |
| Genre | : Mathematics |
| ISBN | : 3834897221 |
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.
| Author | : Rajendra Bhatia |
| Publisher | : World Scientific |
| Total Pages | : 4137 |
| Release | : 2011-06-06 |
| Genre | : Mathematics |
| ISBN | : 9814462934 |
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
| Author | : |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 694 |
| Release | : 1994-02-28 |
| Genre | : Mathematics |
| ISBN | : 0821827987 |
'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.
