Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/21596
Title: Chevalley-Weil formula for hypersurfaces in Pⁿ -bundles over curves and Mordell—Weil ranks in function field towers
Authors: Kloosterman, Remke
Keywords: Elliptic surfacesMordell—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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