Skip's preprints, publications, etc.

Updated 4 June 2009

I study linear algebraic groups, their representations (20G05), and their cohomology (11E72), mostly over arbitrary fields (20G15). In some sense, this encompasses the classical (11E57) and exceptional groups (17B25?); varieties on which those group act (14Mxx); and traditional algebraic objects like quadratic and hermitian forms (11Exx), algebras with involution (16K20), and Lie algebras (17B10, 17B45). Currently, my research centers on adapting techniques from classical representation theory over the complex numbers to prove new results about algebraic groups over arbitrary fields, including anisotropic groups and fields of bad characteristic.

Preprints (intended for publication)

The versions here are the authoritative ones. You can also find (perhaps less recent copies of) my preprints on the arXiv and the Linear algebraic groups and related structures server.

To appear

Publications

  1. Cohomological invariants: exceptional groups and spin groups (notes for the Lens mini-cours)
    with an appendix by Detlev W. Hoffmann
    Memoirs of the American Mathematical Society 200 (2009), no. 937
    ISBN-10: 0-8218-4404-0 / ISBN-13: 978-0-8218-4404-5
    Buy: (AMS) (Amazon)

  2. Pfister's theorem for orthogonal involutions of degree 12
    with Anne Quéguiner-Mathieu
    Proceedings of the American Mathematical Society 137 (2009), 1215-1222
    Go to     the published version

  3. Discriminant of symplectic involutions (published version)
    with R. Parimala and Jean-Pierre Tignol
    Pure & Applied Mathematics Quarterly 5 #1 (2009), 349-374 (Serre special issue, peer-reviewed)

  4. Orthogonal representations of twisted forms of SL2
    Representation Theory 12 (2008), 435-446
    Go to the published version

  5. Expository article: Somewhat more than governors need to know about trigonometry
    Mathematics Magazine 81 (2008) #3, 191-200.
    This was approximately the content of my talk at the 2006 MAA State Dinner for Georgia at Mercer University

  6. Restricting the Rost invariant to the center
    with Anne Quéguiner-Mathieu
    St. Petersburg Math. J. 19 (2008) #2, 197-213 (MR 2333896)
    [Original: Algebra i Analiz 19 (2007) #2, 52-73]
    Go to the published version

  7. Groups of outer type E6 with trivial Tits algebras
    with Holger P. Petersson
    Transformation Groups 12 #3 (2007), 443-474.
    Go to the published version

  8. Kneser-Tits for a rank 1 form of E6 (after Veldkamp)
    Compositio Mathematica 143 #1 (2007), 191-200 (MR 2295201)
    Go to the published version

  9. Geometries, the principle of duality, and algebraic groups
    with Michael P. Carr
    Expositiones Mathematicae 24 #3 (2006) 195-234
    Go to the published version

  10. Totaro's question on zero-cycles on G2, F4, and E6 torsors
    with Detlev W. Hoffmann
    Journal of the London Mathematical Society 73 #2 (2006) 325-338 (MR 2225489)
    Go to the published version

  11. Unramified cohomology of classifying varieties for exceptional simply connected groups
    Transactions of the American Mathematical Society 358 #1 (2006), 359-371 (MR 2171237 / 2006g:11080)
    Go to the published version

  12. Expository article: The characteristic polynomial and determinant are not ad hoc constructions
    American Mathematical Monthly 111 #9 (2004), 761-778 (MR 2104048 / 2006d:15012)
    Go to the published version

  13. Book: Cohomological invariants in Galois cohomology
    with Alexander Merkurjev and J-P. Serre
    American Mathematical Society University Lecture Series, volume 28
    ISBN: 0-8218-3287-5
    Reviews: (Bull. AMS) (MR 2004f:11034)

    Buy: (AMS) (Amazon)

    List of typos
    Summary table from my talk in Besancon, 2 July 2003

  14. The Rost invariant has trivial kernel for quasi-split groups of low rank
    Commentarii Mathematici Helvetici 76 #4 (2001), 684-711 (MR 2003g:20079)
    Go to the published version

  15. Involutions and trace forms on exterior powers of a central simple algebra
    with Anne Quéguiner-Mathieu and Jean-Pierre Tignol
    Documenta Mathematica 6 (2001), 97-118 (MR 2002k:16034)
    Go to the published version

  16. Clifford algebras of hyperbolic involutions
    Math. Zeit. 236 #2 (2001), 321-349 (MR 2002d:16024)
    Go to the published version

  17. Groups of type E7 over arbitrary fields
    Comm. Algebra 29 #6 (2001), 2689-2710 (MR 2002f:17003)
    Go to the published version

  18. Structurable algebras and groups of type E6 and E7
    J. Algebra 236 #2 (2001), 651-691 (MR 2001m:20069)
    Go to the published version

  19. Twisted flag varieties of trialitarian groups
    Comm. Algebra 27 #2 (1999), 841-856 (MR 2000a:20103)
    Go to the published version

  20. Trialitarian groups and the Hasse principle
    manuscripta mathematica 98 #1 (1999), 97-113 (MR 99m:11049)
    Erratum, 113 #2 (2004), p.267: (dvi) (ps) (pdf)
    Go to the published version of the article or the erratum.

  21. Isotropic trialitarian algebraic groups
    J. Algebra 210 #2 (1998), 385-418 (MR 99k:20092)
    Go to the published version

  22. Galois cohomology of special orthogonal groups
    with Jean-Pierre Tignol and Adrian Wadsworth
    manuscripta mathematica 93 #2 (1997), 247-266 (MR 98k:11039)
    Go to the published version

    (If you are curious about such things: this paper makes my Erdös number 4, via Erdös -> Ernst Straus -> Murray Schacher -> Adrian Wadsworth. The MathSciNet "Collaboration Distance" function reports 3, going through a paper collection credited to S. Chowla, Serre, and others.)

Miscellaneous items (not for publication)