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Homology of the Fermat Tower and Universal Measures for Jacobi Sums

Published online by Cambridge University Press:  20 November 2018

Noriyuki Otsubo
Noriyuki Otsubo*
Affiliation:
Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522 Japan e-mail: otsubo@math.s.chiba-u.ac.jp
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Abstract

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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.

Keywords

11S8011G1511R18Fermat curvesIhara-Anderson theoryJacobi sums

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 624 - 640
Copyright
Copyright © Canadian Mathematical Society 2016

References

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