p-adic point counting:
             Lifting the Frobenius for affine varieties


Abstract:

Many p-adic point counting algorithms need an explicit representation
of a Frobenius endomorphism on some cohomology spaces. In some cases, e.g.
for Kedlaya's algorithm, it is nessesary to find a lifting of the of the
characteristic p Frobenius endomorphism on an affine variety to a
corresponding variety in characteristic zero. The lifting of Frobenius is
then given by (a non-unique) power series and for actual computations one
works with truncations to a given precision. Often, computing this
lifting is the most time consuming step in the algorithm. The new idea
to improve the running time is to compute inductively simple polynomial
liftings modulo p^i.