The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Yi Ouyang

doi:10.1007/s10114-005-0875-z

The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Yi Ouyang

Source

Acta Mathematica Sinica, English Series > 2007 > 23 > 7 > 1163-1172

Abstract

Let $$\mathfrak U_z $$ 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 $$H^0(G_z,\;{\mathfrak U}_z/M{\mathfrak U}_z).$$ 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.