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NON ADDITIVE GEOMETRY

By Shai Haran

Product Image: NON ADDITIVE GEOMETRY

NON ADDITIVE GEOMETRY

By Shai Haran

0 - Default Title
Description
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.
Product details
Number of Pages:
194
Release Date:
2025-06-06
Publication Date:
2025-06-06
Publisher:
World Scientific
Languages:
Original: English
ISBN10:
9819806682
ISBN13:
9789819806683
Weight:
440 g
Height:
157 cm
Width:
235 cm
Thickness:
15 cm
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