RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 1989, Volume 180, Number 5, Pages 625–634 (Mi msb1624)  

On minimal models of algebraic curves

Nguyen Khac Viet


Abstract: Let be an odd prime number. Consider the algebraic curves (normalizations of their projective closures):
$$ x^p+y^p=1, \qquad y^p=x^s(1-x), \quad s=1,…,p-2. $$
Let $\zeta$ be a primitive $p$th root of $1$. The Galois group $\operatorname{Gal}(\mathbf Q_p(\zeta)/\mathbf Q_p)$ acts on the minimal models of these curves over $\mathbf Z_p(\zeta)$. This idea is used here to study their minimal models over $\mathbf Z_p$. The action of $\operatorname{Gal}(\mathbf Q_p(\zeta)/\mathbf Q_p)$, passage to the quotient modulo this action, the resolution of singularities on the quotients, and the contraction of exceptional curves of genus $1$ are described. All of this leads to minimal models of the indicated curves over $\mathbf Z_p$.
Bibliography: 6 titles.

Full text: PDF file (512 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1990, 67:1, 65–74

Bibliographic databases:

UDC: 512.75
MSC: Primary 14E30, 14H25; Secondary 14G20
Received: 07.04.1987

Citation: Nguyen Khac Viet, “On minimal models of algebraic curves”, Mat. Sb., 180:5 (1989), 625–634; Math. USSR-Sb., 67:1 (1990), 65–74

Citation in format AMSBIB
\Bibitem{Ngu89}
\by Nguyen Khac Viet
\paper On minimal models of algebraic curves
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 5
\pages 625--634
\mathnet{http://mi.mathnet.ru/msb1624}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1007466}
\zmath{https://zbmath.org/?q=an:0699.14020}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 1
\pages 65--74
\crossref{https://doi.org/10.1070/SM1990v067n01ABEH002085}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990ED88000004}


Linking options:
  • http://mi.mathnet.ru/eng/msb1624
  • http://mi.mathnet.ru/eng/msb/v180/i5/p625

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:195
    Full text:80
    References:18
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019