Glazebrook, J. F.; Grayson, D. R.; Hewitt, P. R. Galois representations on holomorphic differentials. (English) Zbl 0739.14018 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) Cited in 1 Review 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 PDF BibTeX XML Cite \textit{J. F. Glazebrook} et al., Commun. Algebra 19, No. 5, 1375--1386 (1991; Zbl 0739.14018) Full Text: DOI References: [1] DOI: 10.1090/S0002-9947-1968-0222281-6 · doi:10.1090/S0002-9947-1968-0222281-6 [2] Artin M., Théorèmes de représent abilité pour les espaces algébriques. C.P. 6128, Montréal 101, Canada: (1973) [3] Burnside W., The Theory of Groups of Finite Order (1955) · Zbl 0064.25105 [4] DOI: 10.1007/BF02940687 · Zbl 0009.16001 · doi:10.1007/BF02940687 [5] Conway J., Atlas of Finite Groups (1985) [6] Davenport H., Multiplicative Number Theory (1980) · Zbl 0453.10002 [7] Grothendieck A., Brauer Trees of Sporadic Groups 1 (1957) [8] Hecke E., Abh. math. Sem. Univ. 6 pp 525– (1928) [9] Hewitti P., The paucity of large solvable groups (1989) [10] Kurke H., Henselsche Ringe and algebraische Geometrie 1 (1975) · Zbl 0306.13012 [11] DOI: 10.1007/BF02940718 · Zbl 0011.12203 · doi:10.1007/BF02940718 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.