Periods and Nori Motives, Huber Annette

Автор: Muller-stach, Stefan
Название: Periods and nori motives
ISBN: 331950925X ISBN-13(EAN): 9783319509259
Издательство: Springer
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Цена: 102480.00 T
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Описание: This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori`s abelian category of mixed motives.

Автор: Luis Alvarez-Consul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard
Название: Feynman Amplitudes, Periods and Motives
ISBN: 1470422476 ISBN-13(EAN): 9781470422479
Издательство: Mare Nostrum (Eurospan)
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Цена: 104410.00 T
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Описание: Contains the proceedings of the International Research Workshop on Periods and Motives--A Modern Perspective on Renormalization, held from July 2-6, 2012. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics.

Автор: Bruno Kahn
Название: Zeta and L-Functions of Varieties and Motives
ISBN: 1108703399 ISBN-13(EAN): 9781108703390
Издательство: Cambridge Academ
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Цена: 67590.00 T
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Описание: The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.

Автор: Alain Connes, Matilde Marcolli
Название: Noncommutative Geometry, Quantum Fields and Motives
ISBN: 1470450453 ISBN-13(EAN): 9781470450458
Издательство: Mare Nostrum (Eurospan)
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Цена: 82770.00 T
Наличие на складе: Нет в наличии.
Описание: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces.The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adele class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

Автор: Annette Huber
Название: Mixed Motives and their Realization in Derived Categories
ISBN: 3540594752 ISBN-13(EAN): 9783540594758
Издательство: Springer
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Цена: 41920.00 T
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Описание: The conjectual theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. This text describes the approach to motives via their well-defined realizations, which includes a review of several known cohomology theories.

Автор: Tretkoff, Paula B.
Название: Periods and special functions in transcendence
ISBN: 1786342944 ISBN-13(EAN): 9781786342942
Издательство: World Scientific Publishing
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Цена: 85530.00 T
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Описание: 'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate ... The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi-Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Автор: Atsushi Ichino, Kartik Prasanna
Название: Periods of Quaternionic Shimura Varieties. I.
ISBN: 1470448947 ISBN-13(EAN): 9781470448943
Издательство: Mare Nostrum (Eurospan)
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Цена: 101990.00 T
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Описание: This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.

Автор: Burgos Gil Josй Ignacio, Ebrahimi-Fard Kurusch, Gangl Herbert
Название: Periods in Quantum Field Theory and Arithmetic: Icmat, Madrid, Spain, September 15 - December 19, 2014
ISBN: 3030370305 ISBN-13(EAN): 9783030370305
Издательство: Springer
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Цена: 167700.00 T
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Описание: This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory`` at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

Автор: Goncalo Tabuada
Название: Noncommutative Motives
ISBN: 1470423979 ISBN-13(EAN): 9781470423971
Издательство: Mare Nostrum (Eurospan)
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Цена: 44350.00 T
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Описание: Provides an overview of the advances in the theory of noncommutative motives. Part one is devoted to the study of DG categories from a homotopical viewpoint; part two covers the theory of noncommutative pure motives, noncommutative standard conjectures, and noncommutative motivic Galois groups; the third part is devoted to the theory of noncommutative mixed motives.

Автор: Uwe Jannsen
Название: Mixed Motives and Algebraic K-Theory
ISBN: 3540522603 ISBN-13(EAN): 9783540522607
Издательство: Springer
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Цена: 41920.00 T
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Описание: The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincar duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.

Автор: Denis-Charles Cisinski; Fr?d?ric D?glise
Название: Triangulated Categories of Mixed Motives
ISBN: 3030332446 ISBN-13(EAN): 9783030332440
Издательство: Springer
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Цена: 111790.00 T
Наличие на складе: Нет в наличии.
Описание: The primary aim of this monograph is to achieve part of Beilinson`s program on mixed motives using Voevodsky`s theories of A1-homotopy and motivic complexes.

Автор: Denis-Charles Cisinski; Fr?d?ric D?glise
Название: Triangulated Categories of Mixed Motives
ISBN: 3030332411 ISBN-13(EAN): 9783030332419
Издательство: Springer
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Цена: 111790.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The primary aim of this monograph is to achieve part of Beilinson`s program on mixed motives using Voevodsky`s theories of A1-homotopy and motivic complexes.