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Title: | Chevalley-Weil formula for hypersurfaces in Pⁿ -bundles over curves and Mordell—Weil ranks in function field towers | Authors: | Kloosterman, Remke | Keywords: | Elliptic surfaces; Mordell—Weil rank under base change | Issue Date: | 2018 | Publisher: | EUT Edizioni Università di Trieste | Source: | Remke Kloosterman, "Chevalley-Weil formula for hypersurfaces in Pⁿ-bundles over curves and Mordell—Weil ranks in function field towers", in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 50 (2018)", Trieste, EUT Edizioni Università di Trieste, 2018, pp. 101-123 | Abstract: | Let X be a complex hypersurface in a Pⁿ-bundle over a curve C. Let C'→C be a Galois cover with group G. In this paper we describe the C[G]-structure of $H^p,q$(X x$_{c}$ C C') provided that X x$_{c}$ C' is either smooth or n = 3 and X x$_{c}$ C' has at most ADE singularities. As an application we obtain a geometric proof for an upper bound by Páal for the Mordell—Weil rank of an elliptic surface obtained by a Galois base change of another elliptic surface. |
Type: | Article | URI: | http://hdl.handle.net/10077/21596 | ISSN: | 0049-4704 | eISSN: | 2464-8728 | DOI: | 10.13137/2464-8728/21596 | Rights: | Attribution-NonCommercial-NoDerivatives 4.0 Internazionale |
Appears in Collections: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.50 (2018) |
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