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BuchGebunden
372 Seiten
Englisch
Springererschienen am20.03.20171st ed. 2017
This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori´s abelian category of mixed motives.mehr
Verfügbare Formate
BuchGebunden
EUR64,19
BuchKartoniert, Paperback
EUR48,14
E-BookPDF1 - PDF WatermarkE-Book
EUR139,09

Produkt

KlappentextThis book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori´s abelian category of mixed motives.
Zusammenfassung
First book presenting the theory of Nori motives in detail

Studies the Kontsevich-Zagier theory of periods and its relation to mixed motives

Includes full background as well as many examples

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-319-50925-9
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2017
Erscheinungsdatum20.03.2017
Auflage1st ed. 2017
ReiheErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Seiten372 Seiten
SpracheEnglisch
Gewicht759 g
IllustrationenXXIII, 372 p. 7 illus.
Artikel-Nr.41561259

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
"This book is admirably suited for guiding a course or seminar program on this topic. The authors are to be congratulated on producing an important contribution to the mathematical literature on motives and their application to central problems in algebraic geometry and arithmetic." (Marc Levine, Jahresbericht der Deutschen Mathematiker-Vereinigung, August 13, 2019)
"The book under review provides a detailed account on some of the theory of so-called Nori motives ... . The authors provide a lot of details and background information, making this book very accessible. ... this book is a valuable contribution to the field of motives. Particularly commendable is the attention to detail, which can sometimes be missing in this field riddled with conjectures and folklore results. The expository nature makes this book useful to a wide audience." (Tom Bachmann, zbMATH 1369.14001, 2017)
"This text is both a stimulating introduction and a sound comprehensive reference for anyone interested in the field of motives and periods. ... All things considered, I strongly feel that the authors deserve praise for their valiant work. They have fulfilled their difficult program bravely and efficiently." (Alberto Collino, Mathematical Reviews, 2017)mehr

Schlagworte

Autor

Annette Huber works in arithmetic geometry, in particular on motives and special values of L-functions. She has contributed to all aspects of the Bloch-Kato conjecture, a vast generalization of the class number formula and the conjecture of Birch and Swinnerton-Dyer. More recent research interests include period numbers in general and differential forms on singular varieties.

Stefan Müller-Stach works in algebraic geometry, focussing on algebraic cycles, regulators and period integrals. His work includes the detection of classes in motivic cohomology via regulators and the study of special subvarieties in Mumford-Tate varieties. More recent research interests include periods and their relations to mathematical physics and foundations of mathematics.
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Mitarbeit:Friedrich, Benjamin