Non Additive Geometry - Couverture rigide

Haran, Shai

Couverture rigide

ISBN 10 : 9819806682 ISBN 13 : 9789819806683

Editeur : WSPC, 2025

Synopsis

Non Additive Geometry introduces a groundbreaking approach to arithmetic geometry, replacing traditional structure of commutative rings with Props and Bioperads — algebraic systems that can handle matrix multiplication and block direct sums. These structures allow for a deeper exploration of algebraic geometry, where addition no longer holds as a universal operation, particularly at the critical "Real prime." The book presents an innovative and comprehensive study of this new geometric framework, discussing its implications for arithmetic geometry and its potential applications in physics. Chapters explore topics such as generalized schemes, sheaves, ideals and primes, localization, and higher K-theory, following Grothendieck's pioneering methods while extending them to accommodate the needs of arithmetic. The text also addresses future applications, leaving room for readers to explore new directions and potential breakthroughs. This monograph is essential reading for advanced graduate students, researchers, and professionals in mathematics and theoretical physics interested in the foundations of arithmetic geometry, the role of Props and Bioperads, and their applications to broaden our concept of geometry, and therefore have new geometrical objects, such as the Arithmetical Surface Spec(ℤ ⊗ ℤ), the product of the primes Spec(ℤ) with themselves.

Détails de l'édition

• Éditeur: WSPC
• Date d'édition: 2025
• Langue: anglais
• ISBN 10: 9819806682
• ISBN 13: 9789819806683
• Reliure: Relié
• Nombre de pages: 192
• Coordonnées du fabricant: World Scientific Publishing; https://www.worldscientific.com/; ; 5 Toh Tuck Link; #01-01; 596224; Singapour
• Personne responsable: gpsr@libri.de; gpsr@libri.de; ; Friedensallee 273; Hamburg; 22763; Allemagne