MODNET

Research Training Network in Model Theory

Publications > Preprint server > Preprint Number 557
Preprint Number 557
557. Antoine Chambert-Loir and François Loeser Motivic height zeta functions E-mail: Submission date: 8 February 2013. Abstract: Let \bar C be a projective smooth connected curve over an algebraically
closed field of characteristic zero, let F be its field of functions, let C
be a dense open subset of \bar C. Let X be a projective flat morphism to
C whose generic fiber X_F is a smooth equivariant compactification of G
such that D = X_F \setminus G_F is a divisor with strict normal crossings, let
U be a surjective and flat model of G over C. We consider a motivic
height zeta function, a formal power series with coefficients in a suitable
Grothendieck ring of varieties, which takes into account the spaces of sections
s of X --> \bar C of given degree with respect to (a model of) the
log-anticanonical divisor -K_{X_F}(D) such that s(C) is contained in U.
We prove that this power series is rational, that its “largest pole” is at
Mathematics Subject Classification: Keywords and phrases: |

Last updated: February 21 2013 16:41 | Please send your corrections to: |