Homology of the Fermat Tower and Universal Measures for Jacobi Sums

Otsubo, Noriyuki

Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 624-640

Résumé

We give a precise description of the homology group of the Fermat curve as a cyclic module over a group ring. As an application, we prove the freeness of the profinite homology of the Fermat tower. This allows us to define measures, an equivalent of Anderson's adelic beta functions, in a manner similar to Ihara's definition of $\ell$ -adic universal power series for Jacobi sums. We give a simple proof of the interpolation property using a motivic decomposition of the Fermat curve.

Détail

DOI : 10.4153/CMB-2016-012-0

Mots-clés : 11S80, 11G15, 11R18, Fermat curves, Ihara-Anderson theory, Jacobi sums

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