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ON THE NUMBER OF POINTS OVER FINITE FIELDS ON VARIETIES RELATED TO CLUSTER ALGEBRAS

Published online by Cambridge University Press:  22 December 2010

F. CHAPOTON
F. CHAPOTON*
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, Bâtiment Braconnier, 21 Avenue Claude Bernard, F-69622 Villeurbanne Cedex, France e-mail: [email protected]
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Abstract

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We start here the study of some algebraic varieties related to cluster algebras. These varieties are defined as the fibres of the projection map from the cluster variety to the affine space of coefficients. We compute the number of points over finite fields on these varieties, for all simply laced Dynkin diagrams. We also compute the cohomology with compact support in some cases.

Keywords

14R16G20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 141 - 151
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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