nLab differential Galois theory



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



Paths and cylinders

Homotopy groups

Basic facts




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.


  • 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
  • Anand Pillay, Differential Galois theory I, Illinois J. Math. 42(4) 1998
  • D. Bertrand, A. Pillay, Galois theory, functional Lindemann-Weierstrass, and Manin maps, Pacific J. Math. 281:1 (2016) 51–82 doi

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