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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.

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

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Received: 10.05.2002

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
\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
\jour St. Petersburg Math. J.
\yr 2003
\vol 14
\issue 5
\pages 791--821

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    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
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