Guhan Venkat, Laval University
"An integral Euler system for the Rankin-Selberg product of two supersingular modular forms"
One
can
construct
an
Euler
system,
a
collection
of
Galois cohomology
classes,
associated
to
the
Rankin-Selberg
product
of two
eigenforms.
When
the
forms
are
supersingular,
the
Euler
system has
unbounded
denominators.
In
this
talk,
we
will
explore
how
one can
control
the
growth
of
these
denominators
using
Perrin-Riou's theory
of
higher
rank
Euler
systems.
Bounding
the
denominators enables
us
to
deduce
some
important
results
in
Iwasawa
theory. Time
permitting,
we
will
see
how
the
ideas
can
be
used
to
deduce similar
results
for
the
Symmetric square
representation
of
a supersingular
modular
form.
This
is
based
on
a
joint
work
with
Kazim
Buyukboduk,
Antonio
Lei and
David
Loeffler.
MC 5417