A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let be a finite-dimensional -adic representation of the Galois group of a number field . Then an Euler system for is a collection of cohomology classes for a family of Abelian extensions of , with a relation between and whenever (Rubin 2000, p. 4).
Wiles' proof of Fermat's last theorem via the Taniyama-Shimura conjecture made use of Euler systems.