nLab
Galois representation
Contents
should be merged with Galois module
Context
Representation theory
representation theory
geometric representation theory
Ingredients
Definitions
representation, 2representation, ∞representation

group, ∞group

group algebra, algebraic group, Lie algebra

vector space, nvector space

affine space, symplectic vector space

action, ∞action

module, equivariant object

bimodule, Morita equivalence

induced representation, Frobenius reciprocity

Hilbert space, Banach space, Fourier transform, functional analysis

orbit, coadjoint orbit, Killing form

unitary representation

geometric quantization, coherent state

socle, quiver

module algebra, comodule algebra, Hopf action, measuring
Geometric representation theory

Dmodule, perverse sheaf,

Grothendieck group, lambdaring, symmetric function, formal group

principal bundle, torsor, vector bundle, Atiyah Lie algebroid

geometric function theory, groupoidification

EilenbergMoore category, algebra over an operad, actegory, crossed module

reconstruction theorems
Theorems
Contents
Idea
A Galois representation is a Galois module on a vector space.
See at Galois modules for more.
References
Review of the fact that Galois representations encode local systems are are hence analogs in arithmetic geometry of flat connections in differential geometry includes
 Tom Lovering, Étale cohomology and Galois Representations, 2012 (pdf)
See also at function field analogy.
Last revised on September 24, 2014 at 16:01:06.
See the history of this page for a list of all contributions to it.