Non Additive Geometry

Shai Haran (Technion-israel Institute Of Technology, Israel)

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Hardback

Forthcoming
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English

World Scientific Publishing Co Pte Ltd
29 June 2025

Algebra; Algebraic geometry

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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.

By: Shai Haran (Technion-israel Institute Of Technology Israel)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789819806683
ISBN 10: 9819806682
Pages: 190
Publication Date: 29 June 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming