Counting rational points over number fields on a singular cubic surface

Christopher Frei

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin’s conjecture over the field ℚ. Combining this method with techniques developed by Schanuel, we give a proof of Manin’s conjecture over arbitrary number fields for the singular cubic surface S given by the equation x03 = x1x2x3.
    Original languageEnglish
    Pages (from-to)1451-1479
    Number of pages29
    JournalAlgebra and Number Theory
    Volume7
    Issue number6
    DOIs
    Publication statusPublished - 2013

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