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.
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Non Additive Geometry
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World Scientific Publishing Co Pte Ltd, 2025
ISBN 10: 9819806682
ISBN 13: 9789819806683
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ISBN 10: 9819806682
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Hardcover. Condition: new. Hardcover. 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( ), the product of the primes Spec() with themselves. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9789819806683
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Buch. Condition: Neu. NON ADDITIVE GEOMETRY | Haran Shai | Buch | Englisch | 2025 | World Scientific | EAN 9789819806683 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand. Seller Inventory # 133431765
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Buch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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(¿ ¿ ¿), the product of the primes Spec(¿) with themselves. Seller Inventory # 9789819806683