Deformation ring

In mathematics, a deformation ring is a ring that controls liftings of a representation of a Galois group from a finite field to a local field. In particular for any such lifting problem there is often a universal deformation ring that classifies all such liftings, and whose spectrum is the universal deformation space.

A key step in Wiles's proof of the modularity theorem was to study the relation between universal deformation rings and Hecke algebras.

References

• Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn, eds. (1997), Modular forms and Fermat's last theorem, Berlin, New York: Springer-Verlag, ISBN 978-0-387-94609-2, MR 1638473