Control Theorem for Bloch-Kato's Selmer Groups of p-Adic Representations

摘要

We give a sufficient condition for the Selmer group of the p-adic representation associated to a motive over a number field to be controlled in the cyclotomic Z_p-extension. Then we apply this result to the Selmer group of various Galois representations. For example, we treat the representation of a modular form or the symmetric power of an elliptic curve.