Module of covariants

In algebra, given an algebraic group G, a G-module M and a G-algebra A, all over a field k, the module of covariants of type M is the [math]\displaystyle{ A^G }[/math]-module

[math]\displaystyle{ (M \otimes_k A)^G. }[/math]

where [math]\displaystyle{ -^G }[/math] refers to taking the elements fixed by the action of G; thus, [math]\displaystyle{ A^G }[/math] is the ring of invariants of A.

See also

• Local cohomology

References

• M. Brion, Sur les modules de covariants, Ann. Sci. École Norm. Sup. (4) 26 (1993), 1 21.
• M. Van den Bergh, Modules of covariants, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zurich, 1994), Birkhauser, Basel, pp. 352–362, 1995.