Vijay Patankar, ISI Chennai
“Intersective polynomials and Diophantine approximation”
We
consider
Tate
cycles
on
an
Abelian
variety
A
defined
over
a
sufficiently
large
number
field
K
and
having
complex
multiplication.
We
show
that
there
is
an
effective
bound
C
=
C(A,K)
so
that
to
check
whether
a
given
cohomology
class
is
a
Tate
class
on
A,
it
suffices
to
check
the
action
of
the
Frobenius
automorphisms
at
primes
v
of
K
of
norm
less
than
C.
We
also
show
that
for
a
set
of
primes
v
of
K
of
density
1,
the
space
of
Tate
cycles
on
Av,
the
reduction
of
A
at
v,
is
isomorphic
to
the
space
of
Tate
cycles
on
A
itself.
This
is
a
joint
work
with
V.
Kumar
Murty.