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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 4, Pages 141–162 (Mi izv298)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Brauer group

S. G. Tankeev

Vladimir State University

Abstract: For an arithmetic model $X$ of a Fermat surface or a hyperkahler variety with Betti number $\operatorname{b}_2(V\otimes\bar k)>3$ over a purely imaginary number field $k$, we prove the finiteness of the $l$-components of $\operatorname{Br}'(X)$ for all primes $l\gg 0$. This yields a variant of a conjecture of M. Artin.
If $V$ is a smooth projective irregular surface over a number field $k$ and $V(k)\ne\varnothing$, then the $l$-primary component of $\operatorname{Br}(V)/{\operatorname{Br}(k)}$ is an infinite group for every prime $l$. Let $A^1\to M^1$ be the universal family of elliptic curves with a Jacobian structure of level $N\geqslant 3$ over a number field $k\supset\mathbb Q(e^{2\pi i/N})$. Assume that $M^1(k)\ne\varnothing$. If $V$ is a smooth projective compactification of the surface $A^1$, then the $l$-primary component of $\operatorname{Br}(V)/{\operatorname{Br}(\overline M^1)}$ is a finite group for each sufficiently large prime $l$.

DOI: https://doi.org/10.4213/im298

Full text: PDF file (1701 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2000, 64:4, 787–806

Bibliographic databases:

MSC: 14J20
Received: 22.12.1998

Citation: S. G. Tankeev, “On the Brauer group”, Izv. RAN. Ser. Mat., 64:4 (2000), 141–162; Izv. Math., 64:4 (2000), 787–806

Citation in format AMSBIB
\Bibitem{Tan00}
\by S.~G.~Tankeev
\paper On the Brauer group
\jour Izv. RAN. Ser. Mat.
\yr 2000
\vol 64
\issue 4
\pages 141--162
\mathnet{http://mi.mathnet.ru/izv298}
\crossref{https://doi.org/10.4213/im298}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794598}
\zmath{https://zbmath.org/?q=an:0983.14006}
\elib{http://elibrary.ru/item.asp?id=13351720}
\transl
\jour Izv. Math.
\yr 2000
\vol 64
\issue 4
\pages 787--806
\crossref{https://doi.org/10.1070/im2000v064n04ABEH000298}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165984800005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645403281}


Linking options:
  • http://mi.mathnet.ru/eng/izv298
  • https://doi.org/10.4213/im298
  • http://mi.mathnet.ru/eng/izv/v64/i4/p141

    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

    This publication is cited in the following articles:
    1. S. G. Tankeev, “On the Brauer group of an arithmetic scheme”, Izv. Math., 65:2 (2001), 357–388  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. S. V. Tikhonov, V. I. Yanchevskii, “The indices of central simple algebras over function fields of projective spaces over $P_{n,r}$-fields”, Sb. Math., 193:11 (2002), 1691–1705  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. G. Tankeev, “On the Brauer group of an arithmetic scheme. II”, Izv. Math., 67:5 (2003), 1007–1029  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. G. Tankeev, “On the Conjectures of Artin and Shafarevich–Tate”, Proc. Steklov Inst. Math., 241 (2003), 238–248  mathnet  mathscinet  zmath
    5. T. V. Zasorina, “On the Brauer group of an algebraic variety over a finite field”, Izv. Math., 69:2 (2005), 331–343  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:223
    Full text:102
    References:22
    First page:1

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