This article is cited in 1 paper

The Chevalley–Weil Formula for Orbifold Curves

Luca Candelori

Department of Mathematics, University of Hawaii at Manoa, Honolulu, HI, USA

Abstract: In the 1930s Chevalley and Weil gave a formula for decomposing the canonical representation on the space of differential forms of the Galois group of a ramified Galois cover of Riemann surfaces. In this article we prove an analogous Chevalley–Weil formula for ramified Galois covers of orbifold curves. We then specialize the formula to the case when the base orbifold curve is the (reduced) modular orbifold. As an application of this latter formula we decompose the canonical representations of modular curves of full, prime level and of Fermat curves of arbitrary exponent.

Keywords: orbifold curves; automorphisms; modular curves; Fermat curves.

MSC: 14H30; 14H37; 14H45

Received: December 8, 2017; in final form July 2, 2018; Published online July 17, 2018

Language: English

DOI: 10.3842/SIGMA.2018.071

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