### Reduction of abstract homomorphisms of lattices mod p and rigidity, by Chandrashekhar Khare and Dipendra Prasad

In this paper we pose and answer the following question in a few different
contexts: Given a homomorphism f:L_1 -----> L_2 of a
``lattices'' that ``reduces mod p'' for almost all primes p,
is f ``algebraic''? For instance the lattices may be the Mordell-Weil
lattices of rational points of abelian varieties
over Q, or arithmetic groups etc. Implicit in an affirmative
answer to the question for Mordell-Weil lattices is
a novel criterion for abelian varities to be isogenous.

Chandrashekhar Khare and Dipendra Prasad <shekhar@math.utah.edu, dprasad@mri.ernet.in>