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Zap. Nauchn. Sem. POMI, 2010, Volume 377, Pages 141–147 (Mi znsl3819)  

This article is cited in 3 scientific papers (total in 3 papers)

Curves over every global field violating the local-global principle

B. Poonen

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract: There is an algorithm that takes as input a global field $k$ and produces a curve over $k$ violating the local-global principle. Also, given a global field $k$ and a nonnegative integer $n$, one can effectively construct a curve $X$ over $k$ such that $#X(k)=n$. Bibl. 26 titles.

Key words and phrases: Hasse principle, local-global principle, Dem'janenko–Manin method.

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English version:
Journal of Mathematical Sciences (New York), 2010, 171:6, 782–785

Document Type: Article
UDC: 512.772.7
Received: 14.05.2010
Language: English

Citation: B. Poonen, “Curves over every global field violating the local-global principle”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 141–147; J. Math. Sci. (N. Y.), 171:6 (2010), 782–785

Citation in format AMSBIB
\Bibitem{Poo10}
\by B.~Poonen
\paper Curves over every global field violating the local-global principle
\inbook Studies in number theory. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 377
\pages 141--147
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3819}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 6
\pages 782--785
\crossref{https://doi.org/10.1007/s10958-010-0182-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650053701}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Harpaz Y., Skorobogatov A.N., “Singular Curves and the Etale Brauer-Manin Obstruction For Surfaces”, Ann. Sci. Ec. Norm. Super., 47:4 (2014), 765–778  crossref  mathscinet  zmath  isi  elib  scopus
    2. Colliot-Thelene J.-L., Pal A., Skorobogatov A.N., “Pathologies of the Brauer?Manin obstruction”, Math. Z., 282:3-4 (2016), 799–817  crossref  mathscinet  zmath  isi  elib  scopus
    3. Clark P.L., Stankewicz J., “Hasse Principle Violations For Atkin-Lehner Twists of Shimura Curves”, Proc. Amer. Math. Soc., 146:7 (2018), 2839–2851  crossref  mathscinet  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
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