05117nam 22007455 450 991025429270332120200701123334.010.1007/978-3-319-50926-6(CKB)3710000001095336(DE-He213)978-3-319-50926-6(MiAaPQ)EBC4821290(PPN)199767165(EXLCZ)99371000000109533620170309d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierPeriods and Nori Motives /by Annette Huber, Stefan Müller-Stach1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XXIII, 372 p. 7 illus.) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;653-319-50925-X 3-319-50926-8 Includes bibliographical references and index.Part I Background Material -- General Set-Up -- Singular Cohomology -- Algebraic de Rham Cohomology -- Holomorphic de Rham Cohomology -- The Period Isomorphism -- Categories of (Mixed) Motives -- Part II Nori Motives -- Nori's Diagram Category -- More on Diagrams -- Nori Motives -- Weights and Pure Nori Motives -- Part III Periods -- Periods of Varieties -- Kontsevich–Zagier Periods -- Formal Periods and the Period Conjecture -- Part IV Examples -- Elementary Examples -- Multiple Zeta Values -- Miscellaneous Periods: an Outlook.This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;65Number theoryAlgebraic geometryK-theoryAlgebraic topologyCategory theory (Mathematics)Homological algebraAssociative ringsRings (Algebra)Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019K-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Number theory.Algebraic geometry.K-theory.Algebraic topology.Category theory (Mathematics).Homological algebra.Associative rings.Rings (Algebra).Number Theory.Algebraic Geometry.K-Theory.Algebraic Topology.Category Theory, Homological Algebra.Associative Rings and Algebras.512.7Huber Annetteauthttp://id.loc.gov/vocabulary/relators/aut61000Müller-Stach Stefanauthttp://id.loc.gov/vocabulary/relators/autBOOK9910254292703321Periods and Nori Motives1562333UNINA