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Homology theory --- Mathematical physics --- Homology theory. --- Mathematical physics. --- Homologia --- Física matemàtica

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Homologia --- Cohomology operations. --- Algebraic topology. --- Cohomologia --- Teoria de l'homologia --- Teoria de la cohomologia --- Geometria algebraica --- Topologia algebraica --- Àlgebra homològica --- K-teoria --- Teoria dels feixos --- Topology --- Operations (Algebraic topology) --- Algebraic topology

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Topologia algebraica --- Topologia --- Àlgebres de Hopf --- Grau topològic --- Grups fonamentals (Matemàtica) --- K-teoria --- Homologia --- Successions espectrals (Matemàtica) --- Teoria dels feixos --- Topologia de baixa dimensió --- Topologia algebraica.

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This book carefully presents a unified treatment of equivariant Poincaré duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere. The approach used here allows the parallel treatment of both equivariant and nonequivariant cases. It also makes it possible to replace the usual field of coefficients for cohomology, the field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant) de Rham cohomology to the usual singular (equivariant) cohomology . The book will be of interest to graduate students and researchers wanting to learn about the equivariant extension of tools familiar from non-equivariant differential geometry.

Algebraic topology. --- Topology. --- Category theory (Mathematics). --- Homological algebra. --- Group theory. --- Algebra. --- Field theory (Physics). --- Algebraic Topology. --- Category Theory, Homological Algebra. --- Group Theory and Generalizations. --- Field Theory and Polynomials. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Duality theory (Mathematics) --- Cohomology operations. --- Operations (Algebraic topology) --- Algebraic topology --- Teoria de la dualitat (Matemàtica) --- Homologia --- Cohomologia --- Teoria de l'homologia --- Teoria de la cohomologia --- Geometria algebraica --- Topologia algebraica --- Àlgebra homològica --- K-teoria --- Teoria dels feixos --- Dualitat (Matemàtica) --- Principi de dualitat (Matemàtica) --- Principi de la dualitat (Matemàtica) --- Àlgebra --- Topologia

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Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

Number theory. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Algebra --- Arakelov theory. --- Arakelov geometry --- Arithmetical algebraic geometry --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes