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 classesfor 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.
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).