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Chevalley-Weil formula for hypersurfaces in Pⁿ -bundles over curves and Mordell—Weil ranks in function field towers
Kloosterman, Remke
2018
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e-ISSN
2464-8728
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.
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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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