Algebraic Spaces and Stacks

Author: Martin Olsson

Publisher: American Mathematical Soc.

ISBN: 1470427982

Category: Algebraic spaces

Page: 298

View: 6959

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This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
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Algebraic Spaces and Stacks

Author: Martin Olsson

Publisher: American Mathematical Soc.

ISBN: 1470427982

Category: Algebraic spaces

Page: 298

View: 3414

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This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
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Rational Points on Varieties

Author: Bjorn Poonen

Publisher: American Mathematical Soc.

ISBN: 1470437732

Category: Algebraic varieties

Page: 337

View: 4062

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This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
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Moduli of Curves

CIMAT Guanajuato, Mexico 2016

Author: Leticia Brambila Paz,Ciro Ciliberto,Eduardo Esteves,Margarida Melo,Claire Voisin

Publisher: Springer

ISBN: 3319594869

Category: Mathematics

Page: 242

View: 9870

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Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. The book collects the lecture notes of a number of leading algebraic geometers and in particular specialists in the field of moduli spaces of curves and their geometry. This is an important subject in algebraic geometry and complex analysis which has seen spectacular developments in recent decades, with important applications to other parts of mathematics such as birational geometry and enumerative geometry, and to other sciences, including physics. The themes treated are classical but with a constant look to modern developments (see Cascini, Debarre, Farkas, and Sernesi's contributions), and include very new material, such as Bridgeland stability (see Macri's lecture notes) and tropical geometry (see Chan's lecture notes).
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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author: I͡U. I. Manin,Yuri I. Manin,︠I︡U. I. Manin,隝霼. I.·Manin,Kilu I Manin

Publisher: American Mathematical Soc.

ISBN: 0821819178

Category: Mathematics

Page: 303

View: 1903

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The author was once the director of the Max-Planck-Institut fur Mathematik in Bonn, Germany, one of the most prestigious mathematics institutions in the world. Topic expands into the realm of physics, and can be placed in a physics section. The Colloquium series offers classics in the mathematical literature, and can be favorably compared to books now being published in the AMS Chelsea series.
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Arithmetic and Geometry Around Quantization

Author: Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli

Publisher: Springer Science & Business Media

ISBN: 0817648313

Category: Mathematics

Page: 292

View: 1855

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This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.
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Symplectic, Poisson, and Noncommutative Geometry

Author: Tohru Eguchi,Yakov Eliashberg,Yoshiaki Maeda

Publisher: Cambridge University Press

ISBN: 1107056411

Category: Mathematics

Page: 344

View: 3797

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Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and comprehensive reviews, including recent developments in these areas.
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Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author: I͡U. I. Manin,Yuri I. Manin,︠I︡U. I. Manin,隝霼. I.·Manin,Kilu I Manin

Publisher: American Mathematical Soc.

ISBN: 0821819178

Category: Mathematics

Page: 303

View: 495

DOWNLOAD NOW »

The author was once the director of the Max-Planck-Institut fur Mathematik in Bonn, Germany, one of the most prestigious mathematics institutions in the world. Topic expands into the realm of physics, and can be placed in a physics section. The Colloquium series offers classics in the mathematical literature, and can be favorably compared to books now being published in the AMS Chelsea series.
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