Rahim Moosa, Pure Mathematics, University of Waterloo
"Twisted Lang-Weil and the elementary theory of the Frobenius automorphism"
I
will
give
an
expository
talk
on
a
theorem
of
Ehud
Hrushovski
that
is
as
yet
unpublished,
though
an
early
draft
dates
back
at
least
to
1998.
It
is
a
generalisation
of
a
celebrated
classical
theorem
of
Ax
on
the
elementary
theory
of
finite
fields.
Where
Ax’s
theorem
relied
heavily
on
the
Lang-Weil
estimates
for
the
number
of
rational
points
on
varieties
over
finite
fields,
Hrushovski
requires
a
significantly
stronger
intersection-theoretic
twisted
form
of
Lang-Weil.
Besides
motivation
and
precise
statements,
I
will
also
discuss
some
application
of
Hrushovski’s
work
to
algebraic
dynamics
(results
of
Amerik
and
Fakhruddin).
The
material
from
this
talk
is
drawn
from
various
lectures
given
two
weeks
ago
at
CIRM
(Luminy).