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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 141–147 (Mi znsl3819)  
This article is cited in 6 scientific papers (total in 6 papers)

Curves over every global field violating the local-global principle

B. Poonen

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Full-text PDF (564 kB) Citations (6)
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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.
Received: 14.05.2010
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 171, Issue 6, Pages 782–785
DOI: https://doi.org/10.1007/s10958-010-0182-9
Bibliographic databases:
Document Type: Article
UDC: 512.772.7
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650053701}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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