 
Summary: Visibility of ShafarevichTate
groups #
Amod Agashe
University of Texas, Austin
January 8, 2001
# These slides can be obtained from
http://www.math.utexas.edu/~amod/mymath.html
Denition of visibility
K = a number eld
E = an elliptic curve over K
X(E) = ShafarevichTate group of E
= isomorphism classes of torsors for E
that are locally trivial everywhere
B. Mazur: how can one \visualize" the curves
of genus 1 that represent elements of X(E)?
Suppose we are given an embedding over K
of E into an abelian variety J.
Denition 1 (Mazur, at AWS 98).
An element # of X(E/K) is said to be visible
