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Oberseminar WiSe 2008/09 Zusammenfassung des Vortrags von R. Kloosterman

Computing the zeta function of hypersurfaces with defect

The first part of this talk will be an overview of approaches to the computation of the zeta function of varieties over finite fields. One of them is Lauder-Gerkmann's deformation method, which can be used to calculate the zeta function of smooth hypersurfaces.

In the second part of this talk we will propose an extension of the deformation method that applies to the computation of the zeta function of hypersurfaces Y with (strongly) isolated weighted homogeneous hypersurface singularities.

The main difference with the original deformation algorithm lies in the fact that one needs to develop an approach to compute the Frobenius action on Hn+1(Y).