Étale and crystalline beta and gamma functions via Fontaine's periods

  • Francesco Baldassarri

    Università di Padova, Italy

Abstract

We compare the Ihara–Anderson theory of the -adic étale beta function, which describes the Galois action on -adic étale homology for the tower of Fermat curves over of degree a power of , with the crystalline theory of Dwork–Coleman, based on the calculation of the Frobenius action on -adic de Rham cohomology of the same curves. The two constructions are easily related via a ramified extension of Fontaine's period ring contained in , namely . We propose, but do not carry out, a similar comparison for the -adic étale gamma function of Anderson and the Morita–Dwork–Coleman -adic crystalline gamma function.

Cite this article

Francesco Baldassarri, Étale and crystalline beta and gamma functions via Fontaine's periods. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 2, pp. 175–198

DOI 10.4171/RLM/462