The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Let Uz be the universal norm distribution and M a fixed power of prime p. By using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurring in the canonical basis in the cohomology group H0(Gz,Uz/MUz). We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in the theory of Euler systems. One certainly hopes this could lead to a new way to find new Euler systems.