arithmetic differential geometry in nLab
a closed monoidal category. Embedding of diffeological spaces into higher differential geometry. In the last section we saw the embedding of ...
Differential geometry · Perturbative quantum field theory · Physics in Higher Geometry: Motivation and Survey · Hamilton-Jacobi-Lagrange mechanics ...
higher arithmetic geometry, E-∞ arithmetic geometry · number · natural ... differential algebraic K-theory. Contents. 1. Idea; 2. Related ...
An “arithmetic type theory” has now been formalized Vickers 2018 by adjoining such type constructors to coherent logic. Categorically, it ...
Higher geometry or homotopical geometry is the study of concepts of space and geometry in the context of higher category theory and homotopy theory.
Since smooth functions on smooth manifolds are the subject of differential geometry, and since spaces of smooth functions are naturally ...
geometry of physics -- perturbative quantum field theory in nLab
The geometry of physics is differential geometry. This is the flavor of geometry which is modeled on Cartesian spaces ℝ n ...
ordinary algebraic geometry is the study of structured (∞,1)-toposes for the Zariski or etale geometry 𝒢 Zar \mathcal{G}_{Zar} , 𝒢 et \mathcal{G}_{ ...
In its application to physics, symplectic geometry is the fundamental mathematical language for Hamiltonian mechanics, geometric quantization, ...
Very relevant for quantization is also the geometric study of differential operators (see D-geometry, diffiety) and distributions (cf.
Riemannian geometry studies smooth manifolds that are equipped with a Riemannian metric: Riemannian manifolds. Riemannian geometry is hence ...
3. Related concepts · surface · differential geometry of curves and surfaces · singular point of a curve · torsion of a curve · surface, hypersurface.
For instance for T = T = CartSp we have that T T -algebras are smooth algebras and the geometry modeled on them is synthetic differential geometry. This ...
As ordinary differential geometry studies spaces – smooth manifolds – that locally look like vector spaces, supergeometry studies spaces ...
In view of this, in the context of arithmetic differential equations the Fermat quotient is interpreted as an analog in arithmetic geometry of ...
A surface is a space of dimension 2. In differential geometry this means a 2-dimensional smooth manifold or something thereby parametrized.
Shoshichi Kobayashi, Transformation Groups in Differential Geometry 1972, reprinted as: Classics in Mathematics Vol. 70, Springer 1995 (doi ...
Contents. 1. General; 2. In differential geometry; 3. In number theory and algebraic geometry; 4. References. In ...
Yuri Manin, Matilde Marcolli, Holography principle and arithmetic of algebraic curves, Adv. Theor. Math. Phys. 5 (2002) 617-650 (arXiv:hep-th/ ...
nLab mathematicscontents · geometry · general topology · differential topology · differential geometry · algebraic geometry · noncommutative algebraic ...