An arithmetic Riemann--Roch theorem for weighted pointed curves
Anna von Pippich (Darmstadt)
What |
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When |
Dec 11, 2014 from 03:30 pm to 04:30 pm |
Where | Mainz, 05-432 (Hilbertraum) |
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Abstract. In this talk, we report on work in progress with Gerard Freixas generalizing
the arithmetic Riemann--Roch theorem for pointed stable curves to the case
where the metric is allowed to have conical singularities at the marked points.
One main analytical ingredient in the proof is the computation of special values
of certain spectral zeta functions associated to these points.
As particular arithmetic application we derive an analytic class number formula
for the Selberg zeta function of the group $\mathrm{PSL}_2(\mathbb{Z})$.