A-modules
A01=Shai Haran
Abelian Groups
Additive Structures
Affine Schemes
Algebraic Geometry
Algebraic Groups
Algebraic Number Theory
Algebraic Structures
Algebraic Structures in Physics
Algebraic Topology
Arithmetic Geometry
Arithmetical Surface
Author_Shai Haran
Beta Integrals
Bioperads
Block Direct Sum
Categorical Objects
Categorical Sums
Category=PBF
Category=PBMW
Classical Theorems
Combinatorics in Geometry
Commutative Algebra
Commutativity
Compact Topological Spaces
Compactification
Compactification of Spec(Z)
Complex Integers
Complex Prime
Cotangent Complex
Cyclotomic Fields
Cyclotomic Polynomials
Derivations
Derived Algebra
Derived Categories
Derived Functors
Eigenvalues and Eigenvectors
Eigenvalues of Matrices
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact Sequences
Fiber Products
Finite Matrices
Frobenius Operators
Function Fields
Function Theory
Functors
Gelfand's Theorem
Generalized Algebraic Structures
Generalized Schemes
Grothendieck Geometry
Grothendieck Topology
Higher K-Theory
Homological Algebra
Homotopy Groups
Homotopy Theory
Isometries
K-Theory
Localization
Localization of Rings
Matrix Multiplication
Matrix Operations
Matrix Theory
Meromorphic Functions
Modular Arithmetic
Module Theory
Monoidal Categories
Non Additive Geometry
Non-commutative Algebra
Number Fields
Number Theory
Operads
Pro-Schemes
Projective Geometry
Props
Quantum Mechanics
Quantum Relativity
Quillen Model categories
Ramanujan Sums
Ramanujan Zeta sums
Real Integers
Real Prime
Riemann's Zeta Function
Rings and Ideals
Sheaves
Simplicial Objects
Special Lambda Ring
Spectral Theory
Spectrum of a Ring
Stable Homotopy Theory
Symmetric Groups
Symmetric Monoidal Categories
Symmetric Operads
Symmetric Spectra
Tensor Products
Theoretical Physics
Theories of Addition
Topological Hochschild Homology
Topological Spaces
Topology of Schemes
Valuations
Witt Ring
Zariski Topology
Zeta Functions
Product details
- ISBN 9789819806683
- Publication Date: 08 Jul 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
