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portada Non Additive Geometry
Type
Physical Book
Publisher
Author
Language
English
Pages
190
Format
Hardcover
ISBN13
9789819806683

Non Additive Geometry

Shai Haran (Author) · World Scientific Publishing Company · Hardcover

Non Additive Geometry - Shai Haran

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Synopsis "Non Additive Geometry"

Non Additive Geometry introduces a groundbreaking approach to arithmetic geometry, replacing traditional structure of a 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 data, such asSpec(�� ⊗ ��).

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