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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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##### References:
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