Skip's preprints, publications, etc.

Updated 7 February 2010

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. Expository article: Finding good bets in the lottery, and why you shouldn't take them (preprint version) (published version)
    with Aaron Abrams
    American Mathematical Monthly 117 #1 (2010), 3--26

  2. Vanishing of trace forms in low characteristics (preprint version) (published version)
    with an appendix by Alexander Premet
    Algebra & Number Theory 3 #5 (2009), 543-566

  3. Algebraic groups with few subgroups (preprint version) (published version)
    with Philippe Gille
    Journal of the London Math. Society 80 (2009) 405-430

  4. Orthogonal involutions on algebras of degree 16 and the Killing form of E8 (preprint version)
    with an appendix by Kirill Zainoulline
    Slides from my talk at the Chile conference in December 07
    in "Quadratic forms--algebra, arithmetic, and geometry" (R. Baeza, W.K. Chan, D.W. Hoffmann, and R. Schulze-Pillot, eds.), Contemporary Mathematics 493 (2009), 131-162.

  5. 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)

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

  7. 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)

  8. Orthogonal representations of twisted forms of SL2 (preprint version) (published version)
    Representation Theory 12 (2008), 435-446

  9. 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

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

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

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

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

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

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

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

  17. 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

  18. 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

  19. 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

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

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

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

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

  24. 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.

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

  26. 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)