RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






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


Algebra i Analiz, 2002, Volume 14, Issue 5, Pages 110–151 (Mi aa900)  

This article is cited in 13 scientific papers (total in 13 papers)

Research Papers

Invariants of quasitrivial tori and the Rost invariant

A. S. Merkurjeva, R. Parimalab, J.-P. Tignolc

a Department of Mathematics, University of California, Los Angeles California
b School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
c Institut de Mathématique Pure et Appliquée, Université catholique de Louvain, Louvain-la-Neuve, Belgium

Abstract: For any absolutely simple, simply connected linear algebraic group $G$ over a field $F$. Rost has defined invariants for the torsors under $G$ with values in the Galois cohomology group $H^3(F,\mathbb Q/\mathbb Z(2))$. In this paper, an explicit description of these invariants is given for the torsors induced from the center of $G$ in the case where $G$ is of type $A_n$ or $D_n$. As an application, it is shown that the multipliers of the unitary similitudes satisfy a relation involving the discriminant algebra.

Full text: PDF file (1704 kB)

English version:
St. Petersburg Mathematical Journal, 2003, 14:5, 791–821

Bibliographic databases:
Received: 10.05.2002
Language:

Citation: A. S. Merkurjev, R. Parimala, J.-P. Tignol, “Invariants of quasitrivial tori and the Rost invariant”, Algebra i Analiz, 14:5 (2002), 110–151; St. Petersburg Math. J., 14:5 (2003), 791–821

Citation in format AMSBIB
\Bibitem{MerParTig02}
\by A.~S.~Merkurjev, R.~Parimala, J.-P.~Tignol
\paper Invariants of quasitrivial tori and the Rost invariant
\jour Algebra i Analiz
\yr 2002
\vol 14
\issue 5
\pages 110--151
\mathnet{http://mi.mathnet.ru/aa900}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1970336}
\zmath{https://zbmath.org/?q=an:1041.11023}
\transl
\jour St. Petersburg Math. J.
\yr 2003
\vol 14
\issue 5
\pages 791--821


Linking options:
  • http://mi.mathnet.ru/eng/aa900
  • http://mi.mathnet.ru/eng/aa/v14/i5/p110

    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. Berhuy G., Monsurro M., Tignol J.-P., “Cohomological invariants and $R$-triviality of adjoint classical groups”, Math. Z., 248:2 (2004), 313–323  crossref  mathscinet  zmath  isi  scopus
    2. Garibaldi S., “Unramified cohomology of classifying varieties for exceptional simply connected groups”, Trans. Amer. Math. Soc., 358:1 (2006), 359–371 (electronic)  crossref  mathscinet  zmath  isi  scopus
    3. St. Petersburg Math. J., 19:2 (2008), 197–213  mathnet  crossref  mathscinet  zmath  isi
    4. Berhuy G., “Cohomological invariants of quaternionic skew-Hermitian forms”, Arch. Math. (Basel), 88:5 (2007), 434–447  crossref  mathscinet  zmath  isi  scopus
    5. Kulshrestha A., Parimala R., “$R$-equivalence in adjoint classical groups over fields of virtual cohomological dimension 2”, Trans. Amer. Math. Soc., 360:3 (2008), 1193–1221 (electronic)  crossref  mathscinet  zmath  isi  elib  scopus
    6. Garibaldi S., Cohomological invariants: exceptional groups and spin groups, Mem. Amer. Math. Soc., 200, no. 937, 2009, xii+81 pp.  mathscinet  isi
    7. Garibaldi S., “Orthogonal involutions on algebras of degree 16 and the Killing form of E-8”, Quadratic Forms - Algebra, Arithmetic, and Geometry, Contemporary Mathematics, 493, 2009, 131–162  crossref  mathscinet  zmath  isi
    8. Gille Ph., Queguiner-Mathieu A., “Formula for Rost invariants”, Algebra & Number Theory, 5:1 (2011), 1–35  crossref  mathscinet  zmath  isi  scopus
    9. Preeti R., “Classification Theorems for Hermitian Forms, the Rost Kernel and Hasse Principle Over Fields with Cd(2)(K) <= 3”, J. Algebra, 385 (2013), 294–313  crossref  mathscinet  zmath  isi  scopus
    10. Bermudez H. Ruozzi A., “Degree 3 Cohomological Invariants of Split Simple Groups That Are Neither Simply Connected Nor Adjoint”, J. Ramanujan Math. Soc., 29:4 (2014), 465–481  mathscinet  zmath  isi
    11. Preeti R., Soman A., “Adjoint groups over ${\mathbb Q}_p (X)$ and R-equivalence - revisited”, Proc. Amer. Math. Soc., 145:3 (2017), 1019–1029  crossref  mathscinet  zmath  isi  scopus
    12. Garibaldi S. Merkurjev A.S., “Rost Invariant of the Center, Revisited”, Pac. J. Math., 291:2 (2017), 369–397  crossref  mathscinet  zmath  isi  scopus
    13. Merkurjev A.S., “Degree Three Unramified Cohomology of Adjoint Semisimple Groups”, Math. Z., 289:3-4 (2018), 1089–1119  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:521
    Full text:141
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020