  The slope filtration of Euclidean lattices was introduced in works by Stuhler
in the late 1970s, extended by Grayson a few years later, as a new tool for
reduction theory and its applications to the study of arithmetic groups.
Lattices with trivial filtration are called semistable, in keeping with a
classical terminology. In 1997, Bost conjectured that the tensor product of
semistable lattices should be semistable itself. Our aim in this work is to
study these questions for the restricted class of isodual lattices. Such
lattices appear in a wide range of contexts, and it is rather natural to study
their slope filtration. We exhibit specific properties in this case, which
allow, in turn, to prove some new particular cases of Bost's conjecture.
