Galois representations on holomorphic differentials. (English) Zbl 0739.14018

Glazebrook, J. F.; Grayson, D. R.; Hewitt, P. R.

Commun. Algebra 19, No. 5, 1375-1386 (1991).

Let \(C\) be a complete \(\mathbb{C}\)-algebraic curve of genus \(g\) and let \(G\) be a finite group which acts faithfully on \(C\). The authors establish a formula which describes \(H^ 0(C,(\Omega^ 1_ C)^{\otimes q})\) as a representation of \(G\) for \(q\geq 1\). Such a formula has been established by Chevalley and Weil. Here it is reproved with the language of modern algebraic geometry in order to be suitable for certain situations. — Hence some concrete examples have been worked out thoroughly to illustrate this approach.

Reviewer: Vo Van Tan (Boston)

MSC:

14H55	Riemann surfaces; Weierstrass points; gap sequences
14F10	Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
13N10	Commutative rings of differential operators and their modules

Keywords:

action of finite group on algebraic curve; differentials on algebraic curve

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