The mathematical enterprises of Robert Thomason

Weibel, Charles

doi:10.1090/S0273-0979-97-00707-6

The mathematical enterprises of Robert Thomason
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Bull. Amer. Math. Soc. 34 (1997), 1-13 Request permission

Abstract:

During his career, Bob Thomason was involved in an interesting and varied group of mathematical endeavors. This is a retrospective survey of his contributions.

References

Kenneth S. Brown and Stephen M. Gersten, Algebraic $K$-theory as generalized sheaf cohomology, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 266–292. MR 0347943
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573, DOI 10.1007/978-3-540-38117-4
J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609, DOI 10.1007/BFb0068547
William G. Dwyer and Eric M. Friedlander, Étale $K$-theory and arithmetic, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 453–455. MR 648533, DOI 10.1090/S0273-0979-1982-15013-3
William Dwyer, Eric Friedlander, Victor Snaith, and Robert Thomason, Algebraic $K$-theory eventually surjects onto topological $K$-theory, Invent. Math. 66 (1982), no. 3, 481–491. MR 662604, DOI 10.1007/BF01389225
Eric M. Friedlander, Étale $K$-theory. I. Connections with etale cohomology and algebraic vector bundles, Invent. Math. 60 (1980), no. 2, 105–134. MR 586424, DOI 10.1007/BF01405150
Daniel Grayson, Higher algebraic $K$-theory. II (after Daniel Quillen), Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Lecture Notes in Math., Vol. 551, Springer, Berlin, 1976, pp. 217–240. MR 0574096
Henri A. Gillet and Robert W. Thomason, The $K$-theory of strict Hensel local rings and a theorem of Suslin, Proceedings of the Luminy conference on algebraic $K$-theory (Luminy, 1983), 1984, pp. 241–254. MR 772059, DOI 10.1016/0022-4049(84)90037-9
M. Harada, A proof of the Riemann-Roch theorem, Ph.D. thesis, Johns Hopkins University, Baltimore, 1987.
Dana May Latch, Robert W. Thomason, and W. Stephen Wilson, Simplicial sets from categories, Math. Z. 164 (1979), no. 3, 195–214. MR 516607, DOI 10.1007/BF01182267
J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609, DOI 10.1007/BFb0068547
J. P. May and R. Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978), no. 3, 205–224. MR 508885, DOI 10.1016/0040-9383(78)90026-5
Erik K. Pedersen and Charles A. Weibel, $K$-theory homology of spaces, Algebraic topology (Arcata, CA, 1986) Lecture Notes in Math., vol. 1370, Springer, Berlin, 1989, pp. 346–361. MR 1000388, DOI 10.1007/BFb0085239
Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin-New York, 1967. MR 0223432, DOI 10.1007/BFb0097438
Daniel Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295. MR 258031, DOI 10.2307/1970725
Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129
Graeme Segal, Categories and cohomology theories, Topology 13 (1974), 293–312. MR 353298, DOI 10.1016/0040-9383(74)90022-6
M. Artin, A. Grothendieck and J.-L. Verdier, Théorie de Topos et Cohomologie Étale des Schémas (SGA 4), Lecture Notes in Math., vols. 269,270,305, Springer-Verlag, 1972–73.
Théorie des intersections et théorème de Riemann-Roch, Lecture Notes in Mathematics, Vol. 225, Springer-Verlag, Berlin-New York, 1971 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1966–1967 (SGA 6); Dirigé par P. Berthelot, A. Grothendieck et L. Illusie. Avec la collaboration de D. Ferrand, J. P. Jouanolou, O. Jussila, S. Kleiman, M. Raynaud et J. P. Serre. MR 0354655
A. Suslin, Algebraic $K$-theory and Motivic Cohomology, Proc. International Congress of Mathematicians, Zürich 1994, vol. 1, Birkhäuser, 1995, pp. 342–351.
R. W. Thomason, A note on spaces with normal product with some compact space, Proc. Amer. Math. Soc. 44 (1974), 509–510. MR 367923, DOI 10.1090/S0002-9939-1974-0367923-8
R.W. Thomason, Homotopy colimits in $\mathbf {Cat}$, with applications to algebraic $K$-theory and loop space theory, Ph.D. thesis, 124 pages, Princeton University, 1977, available from University Microfilms, Ann Arbor, MI 48104.
R. W. Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 91–109. MR 510404, DOI 10.1017/S0305004100055535
R. W. Thomason, Uniqueness of delooping machines, Duke Math. J. 46 (1979), no. 2, 217–252. MR 534053, DOI 10.1215/S0012-7094-79-04612-X
R. W. Thomason, Cat as a closed model category, Cahiers Topologie Géom. Différentielle 21 (1980), no. 3, 305–324. MR 591388
R. W. Thomason, First quadrant spectral sequences in algebraic $K$-theory, Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Lecture Notes in Math., vol. 763, Springer, Berlin, 1979, pp. 332–355. MR 561229
Robert W. Thomason, First quadrant spectral sequences in algebraic $K$-theory via homotopy colimits, Comm. Algebra 10 (1982), no. 15, 1589–1668. MR 668580, DOI 10.1080/00927878208822794
R. W. Thomason, Beware the phony multiplication on Quillen’s ${\scr A}^{-1}{\scr A}$, Proc. Amer. Math. Soc. 80 (1980), no. 4, 569–573. MR 587929, DOI 10.1090/S0002-9939-1980-0587929-6
R. W. Thomason, Algebraic $K$-theory and étale cohomology, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 3, 437–552. MR 826102, DOI 10.24033/asens.1495
R. W. Thomason, The Lichtenbaum-Quillen conjecture for $K/l_\ast [\beta ^{-1}]$, Current trends in algebraic topology, Part 1 (London, Ont., 1981) CMS Conf. Proc., vol. 2, Amer. Math. Soc., Providence, R.I., 1982, pp. 117–139. MR 686114
R. W. Thomason, Riemann-Roch for algebraic versus topological $K$-theory, J. Pure Appl. Algebra 27 (1983), no. 1, 87–109. MR 680887, DOI 10.1016/0022-4049(83)90032-4
R. W. Thomason, Bott stability in algebraic $K$-theory, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 389–406. MR 862644, DOI 10.1090/conm/055.1/862644
R. W. Thomason, The homotopy limit problem, Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982) Contemp. Math., vol. 19, Amer. Math. Soc., Providence, R.I., 1983, pp. 407–419. MR 711065
R. W. Thomason, Absolute cohomological purity, Bull. Soc. Math. France 112 (1984), no. 3, 397–406 (English, with French summary). MR 794741, DOI 10.24033/bsmf.2014
R. W. Thomason, Algebraic $K$-theory of group scheme actions, Algebraic topology and algebraic $K$-theory (Princeton, N.J., 1983) Ann. of Math. Stud., vol. 113, Princeton Univ. Press, Princeton, NJ, 1987, pp. 539–563. MR 921490
R. W. Thomason, Lefschetz-Riemann-Roch theorem and coherent trace formula, Invent. Math. 85 (1986), no. 3, 515–543. MR 848684, DOI 10.1007/BF01390328
R. W. Thomason, Comparison of equivariant algebraic and topological $K$-theory, Duke Math. J. 53 (1986), no. 3, 795–825. MR 860673, DOI 10.1215/S0012-7094-86-05344-5
R. W. Thomason, Equivariant resolution, linearization, and Hilbert’s fourteenth problem over arbitrary base schemes, Adv. in Math. 65 (1987), no. 1, 16–34. MR 893468, DOI 10.1016/0001-8708(87)90016-8
R. W. Thomason, Equivariant algebraic vs. topological $K$-homology Atiyah-Segal-style, Duke Math. J. 56 (1988), no. 3, 589–636. MR 948534, DOI 10.1215/S0012-7094-88-05624-4
R. W. Thomason, The finite stable homotopy type of some topoi, J. Pure Appl. Algebra 47 (1987), no. 1, 89–104. MR 906404, DOI 10.1016/0022-4049(87)90101-0
R. W. Thomason, A finiteness condition equivalent to the Tate conjecture over $\mathbf F_q$, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987) Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 385–392. MR 991987, DOI 10.1090/conm/083/991987
R. W. Thomason, Survey of algebraic vs. étale topological $K$-theory, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987) Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 393–443. MR 991988, DOI 10.1090/conm/083/991988
Robert W. Thomason, The local to global principle in algebraic $K$-theory, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 381–394. MR 1159226
R. W. Thomason, Une formule de Lefschetz en $K$-théorie équivariante algébrique, Duke Math. J. 68 (1992), no. 3, 447–462 (French). MR 1194949, DOI 10.1215/S0012-7094-92-06817-7
R. W. Thomason, Le principe de scindage et l’inexistence d’une $K$-theorie de Milnor globale, Topology 31 (1992), no. 3, 571–588 (French). MR 1174260, DOI 10.1016/0040-9383(92)90052-J
R. W. Thomason, Les $K$-groupes d’un schéma éclaté et une formule d’intersection excédentaire, Invent. Math. 112 (1993), no. 1, 195–215 (French). MR 1207482, DOI 10.1007/BF01232430
R.W. Thomason, Les $K$-groupes d’un fibré projectif, Algebraic $K$-theory and algebraic topology, NATO ASI Series C, vol. 407, Kluwer, 1993, pp. 243–248.
R.W. Thomason, The classification of triangulated subcategories, preprint (1995), Compositio Math. (1996), to appear.
R.W. Thomason, Symmetric monoidal categories model all connective spectra, Theory Appl. Categories 1 (1995), 78–118, (electronic journal http://www.tac.mta.ca/tac/).
R. W. Thomason and Thomas Trobaugh, Higher algebraic $K$-theory of schemes and of derived categories, The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, Birkhäuser Boston, Boston, MA, 1990, pp. 247–435. MR 1106918, DOI 10.1007/978-0-8176-4576-2_{1}0
Robert W. Thomason and Thomas F. Trobaugh, Le théorème de localisation en $K$-théorie algébrique, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 16, 829–831 (French, with English summary). MR 978249
Robert W. Thomason and W. Stephen Wilson, Hopf rings in the bar spectral sequence, Quart. J. Math. Oxford Ser. (2) 31 (1980), no. 124, 507–511. MR 596982, DOI 10.1093/qmath/31.4.507
Friedhelm Waldhausen, Algebraic $K$-theory of spaces, Algebraic and geometric topology (New Brunswick, N.J., 1983) Lecture Notes in Math., vol. 1126, Springer, Berlin, 1985, pp. 318–419. MR 802796, DOI 10.1007/BFb0074449
C. Weibel, Robert W. Thomason (1952–1995), Notices of the AMS 43 (1996), 860–862.
D. Yao, Higher algebraic $K$-theory of admissible abelian categories and localization theorems, Ph.D. thesis, Johns Hopkins University, Baltimore, 1990.