Geodesic
Homology of the Fermat Tower and Universal Measures for Jacobi Sums
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 624-640

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DOI

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.
DOI : 10.4153/CMB-2016-012-0
Mots-clés : 11S80, 11G15, 11R18, Fermat curves, Ihara-Anderson theory, Jacobi sums 
Otsubo, Noriyuki. Homology of the Fermat Tower and Universal Measures for Jacobi Sums. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 624-640. doi: 10.4153/CMB-2016-012-0
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     title = {Homology of the {Fermat} {Tower} and {Universal} {Measures} for {Jacobi} {Sums}},
     journal = {Canadian mathematical bulletin},
     pages = {624--640},
     year = {2016},
     volume = {59},
     number = {3},
     doi = {10.4153/CMB-2016-012-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-012-0/}
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