nLab
D-geometry

This is a redirection page using the semi-standard term D-geometry for the geometry of D-modules (and closely related perverse sheaves), D-schemes, differential operators and related structures. As equations of mathematical physics are often given by differential equations and the quantization depends much on the fine aspects of the symplectic geometry and D-geometry it may be useful to have some focusing point(s) in $n$lab on our effort to keep notes on this field. For now the material is rather scarce and most of the related entries are stubs:

• regular differential operator, ordinary differential equation

• connection, flat connection, local system, D-module, perverse sheaf

• holonomic D-module, meromorphic connection, characteristic variety

• diffiety, Grothendieck connection, crystal, de Rham space

• synthetic differential geometry, infinitesimal object

• Kähler differential, tangent category, tangent (∞,1)-category, cotangent complex, deformation theory, formally smooth morphism, jet space

• semiclassical approximation, Maslov index, Stokes phenomenon, wall crossing

• microlocal analysis, algebraic microlocalization

• Riemann-Hilbert problem, Fuchsian equation

• algebraic approaches to differential calculus

• regular differential operator in noncommutative geometry

• holonomic quantum field, Hodge theory, algebraic analysis