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Galois representations on holomorphic differentials. (English) Zbl 0739.14018
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.

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
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