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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The split torsor method for Manin’s conjecture
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by Ulrich Derenthal and Marta Pieropan PDF
Trans. Amer. Math. Soc. 373 (2020), 8485-8524

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.
References
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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.
  • © Copyright 2020 by the authors
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 8485-8524
  • MSC (2010): Primary 11D45; Secondary 11G35, 14G05
  • DOI: https://doi.org/10.1090/tran/8133
  • MathSciNet review: 4177266