Summary: Visibility of Shafarevich-Tate
University of Texas, Austin
January 8, 2001
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Denition of visibility
K = a number eld
E = an elliptic curve over K
X(E) = Shafarevich-Tate 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