Breadcrumb
Integral structures in p-adic cohomology
Wed 16 January 2013, 16:00
Andreas Langer
Exeter
Organisers: Tim Dokchitser, Daniel Loughran
ABSTRACT
For an algebraic variety over a finite field of char p one can consider its
zeta-function which encodes the number of rational points of the
variety over finite field extensions. It is known that this zeta-function
is rational, i.e a quotient of polymomials which arise from the Frobenius
action on certain finite-dimensional vector spaces over the field of p-adic numbers.
These vector spaces occur as suitable p-adic cohomology groups and are definedpurely algebraically if the variety is smooth and proper, but involve some p-adic (non-archimedean) analysis otherwise, for example if X is affine. I will explain the definition of these vector spaces and also discuss the problem of integral structures, i.e. to find a canonical lattice in p-adic cohomology.