Let be an elliptic curve over a number field .
Let be either a prime of or a real
Archimedian place (i.e., embedding
).
As in Section 2.2.1 we also obtain
a local Kummer sequence
Putting these together for all we obtain a commutative
diagram:
|
(2.2.2) |
Definition 2.7
The
-Selmer group of an elliptic curve
over a number
field
is
William
2007-05-25