Triangulated Categories in Representation Theory and Beyond
Author: Petter Andreas Bergh
Publisher: Springer Nature
Published:
Total Pages: 275
ISBN-13: 3031577892
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Author: Petter Andreas Bergh
Publisher: Springer Nature
Published:
Total Pages: 275
ISBN-13: 3031577892
DOWNLOAD EBOOKAuthor: Paul Balmer
Publisher:
Published: 2020
Total Pages: 0
ISBN-13: 9783037197097
DOWNLOAD EBOOKThis book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists.The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples and the separable monadicity theorem explains how the value of a Mackey 2-functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology. The second part of the book provides a motivic approach to Mackey 2-functors, 2-categorifying the well-known span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida's crossed Burnside ring are the universal source of block decompositions.The book is self-contained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interestedin category theory, representation theory and topology.
Author: D. Kaledin
Publisher: American Mathematical Society
Published: 2022-11-10
Total Pages: 104
ISBN-13: 1470455366
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Author: Michael Artin
Publisher: American Mathematical Society
Published: 2022-09-21
Total Pages: 104
ISBN-13: 1470471116
DOWNLOAD EBOOKThis book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.
Author: Michael A. Hill
Publisher: Cambridge University Press
Published: 2021-07-29
Total Pages: 881
ISBN-13: 1108831443
DOWNLOAD EBOOKA complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author: Haynes Miller
Publisher: CRC Press
Published: 2020-01-23
Total Pages: 982
ISBN-13: 1351251619
DOWNLOAD EBOOKThe Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Author: PAUL. DELL'AMBROGIO BALMER (IVO.)
Publisher:
Published: 2020
Total Pages:
ISBN-13: 9783037192092
DOWNLOAD EBOOKAuthor: Nitya Kitchloo, Mona Merling
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 208
ISBN-13: 1470437740
DOWNLOAD EBOOKThis 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: Alain Connes
Publisher: Springer
Published: 2003-12-15
Total Pages: 364
ISBN-13: 3540397027
DOWNLOAD EBOOKNoncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author: Stefan Patrikis
Publisher: American Mathematical Soc.
Published: 2019-04-10
Total Pages: 170
ISBN-13: 1470435403
DOWNLOAD EBOOKLet F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.