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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

The split torsor method for Manin’s conjecture


Authors: Ulrich Derenthal and Marta Pieropan
Journal: Trans. Amer. Math. Soc. 373 (2020), 8485-8524
MSC (2010): Primary 11D45; Secondary 11G35, 14G05
DOI: https://doi.org/10.1090/tran/8133
Published electronically: September 29, 2020
MathSciNet review: 4177266
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Abstract: We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin’s conjecture for all nonsplit quartic del Pezzo surfaces of type $\mathbf {A}_{3}+\mathbf {A}_{1}$ over arbitrary number fields. The counting problem on the split torsor is solved in the framework of o-minimal structures.


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Additional Information

Ulrich Derenthal
Affiliation: Leibniz Universität Hannover, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Welfengarten 1, 30167 Hannover, Germany
MR Author ID: 776744
Email: derenthal@math.uni-hannover.de

Marta Pieropan
Affiliation: Utrecht University, Mathematical Institute, Budapestlaan 6, 3584 CD Utrecht, the Netherlands
MR Author ID: 1166273
Email: m.pieropan@uu.nl

Received by editor(s): July 22, 2019
Received by editor(s) in revised form: February 5, 2020
Published electronically: September 29, 2020
Additional Notes: The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft. Some of this work was done while he was on sabbatical leave at the University of Oxford.
The second author was partly supported by grant ES 60/10-1 of the Deutsche Forschungsgemeinschaft.
Article copyright: © Copyright 2020 by the authors