nLab
differential Galois theory

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

Differential Galois theory is an analogue of Galois theory where fields are generalized to differential fields, hence is a theory for differential equations rather than just algebraic equations.

References

  • Pierre Deligne, Catégories Tannakiennes, Grothendieck Festschrift, vol. II, Birkhäuser Progress in Math. 87 (1990) pp.111-195.

  • Andy Magid, Differential Galois theory, Notices of the AMS (1999) pdf

  • Teresa Crespo, The origins of differential Galois theory (pdf slides)

  • Andy R. Magid, Universal covers and category theory in polynomial and differential Galois theory, pdf

Textbook accounts include

  • Marius van der Put, Michael Singer, Galois theory of linear differential equations, Springer, Berlin (2003)

  • M. Singer, Direct and inverse problems in differential Galois theory, in H. Bass, et al. (eds.) Selected works of Ellis Kolchin with commentary , Amer. Math. Soc. 1999, 527–554.

Discussion in terms of D-geometry is in

based on

  • B. H. Matzat, M. van der Put, Iterative differential equations and the Abhyankar conjecture, J. Reine Angew. Math. 557 (2003), pp. 1–52.

A connection to geometric invariant theory is proposed in

Model theoretic aspects are discussed in

  • Moshe Kamensky, Anand Pillay, Interpretations and differential Galois extensions, arxiv/1409.5915

Revised on September 23, 2014 15:06:23 by Zoran Škoda (161.53.130.104)