New York Journal of Mathematics
Volume 18 (2012) 911-924


Ruthi Hortsch

On the canonical representation of curves in positive characteristic

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Published: November 21, 2012
Keywords: Canonical representation, automorphisms of curves, de Rham hypercohomology, positive characteristic
Subject: 14G17 (primary), 11G99 (secondary)

Given a smooth curve, the canonical representation of its automorphism group is given by the natural action of the automorphisms on the space of global regular 1-forms. In this paper, we study an explicit set of curves in positive characteristic with irreducible canonical representation whose genus is unbounded. Additionally, we study the implications this has for the de Rham hypercohomology as a representation of the automorphism group.


This paper was researched and written for an NSF REU under the mentorship of Bryden Cais.

Author information

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139