Infinitesimal cohomology information

In mathematics, infinitesimal cohomology is a cohomology theory for algebraic varieties introduced by Grothendieck (1966). In characteristic 0 it is essentially...

Tors). The idea of crystalline cohomology, roughly, is to replace the Zariski open sets of a scheme by infinitesimal thickenings of Zariski open sets...

homological algebra K-theory Hilbert scheme Homotopy hypothesis Infinitesimal cohomology – cohomology theory for algebraic varieties introduced by Grothendieck...

algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many...

pure operators are graded by integral ghost numbers and we have a BRST cohomology. From a practical perspective, a quantum field theory consists of an action...

from the infinitesimal point of view. Indeed, any Lie group action σ : G × M → M {\displaystyle \sigma :G\times M\to M} induces an infinitesimal Lie algebra...

curve Algebroid cohomology Algebroid multifunction Courant algebroid, an object generalising Lie bialgebroids Lie algebroid, the infinitesimal counterpart...

differential k-form is thought of as measuring the flux through an infinitesimal k-parallelotope at each point of the manifold, then its exterior derivative...

Lie algebras (tangent vectors near the identity) may be thought of as infinitesimal symmetry motions. Thus Lie algebras and their representations are used...

Noetherian schemes. Čech cohomology and sheaf cohomology agree on an affine open cover. This makes it possible to compute the sheaf cohomology of P S n {\displaystyle...

algebras play in the theory of Lie groups: reducing global problems to infinitesimal ones. Indeed, any Lie groupoid gives rise to a Lie algebroid, which...

Borel–Bott–Weil theorem, for the discrete series, using L2 cohomology instead of the coherent sheaf cohomology used in the compact case. An application of the index...

construction of smooth topological invariants of such manifolds, such as de Rham cohomology or the intersection form, as well as smoothable topological constructions...

been used to define other cohomology theories since then, such as ℓ-adic cohomology, flat cohomology, and crystalline cohomology. While Grothendieck topologies...

extend infinitesimal deformations to actual deformations. The modular class of a Poisson manifold is a class in the first Poisson cohomology group, which...

physics.” Kostant, Bertram (1955). "Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold". Trans. Amer. Math. Soc. 80 (2): 528–542...

following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2. They can be seen as an analogue of fibre bundles where the...

(1976): every simply connected closed Riemannian manifold X whose rational cohomology ring is not generated by one element has infinitely many geometrically...

represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. As an example, consider air as it is heated...

Birkhauser 1983. For the étale cohomology version, see the chapter on monodromy in Freitag, E.; Kiehl, Reinhardt (1988), Etale Cohomology and the Weil Conjecture...

computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change. Discrete...

characterized by its Euler class, which is a degree n + 1 {\displaystyle n+1} cohomology class in the total space of the bundle. In the case n = 1 {\displaystyle...