Homology of the Fermat Tower and Universal Measures for Jacobi Sums
Printed: Sep 2016
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 similar manner 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.
Fermat curves, Ihara-Anderson theory, Jacobi sums
11S80 - Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
11G15 - Complex multiplication and moduli of abelian varieties [See also 14K22]
11R18 - Cyclotomic extensions