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The Mathematical Enterprises of Robert Thomason

Author(s): Charles A. Weibel
Journal: Bull. Amer. Math. Soc. 34 (1997), 1-13.
MSC (1991): Primary 19-02; Secondary 18-02, 55-02
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Abstract | References | Similar articles | Additional information

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:

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H. Gillet and R.W. Thomason, The $K$-theory of strict hensel local rings and a theorem of Suslin, J. Pure Appl. Alg. 34 (1984), 241-254. MR 86e:18014

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M. Harada, A proof of the Riemann-Roch theorem, Ph.D. thesis, Johns Hopkins University, Baltimore, 1987.

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D. Latch, R.W. Thomason and S. Wilson, Simplicial sets from categories, Math. Zeit. 164 (1979), 195-214. MR 80e:55012

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J.P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, 1972. MR 54:8623b

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J.P. May and R.W. Thomason, The uniqueness of infinite loop space machines, Topology 17 (1978), 205-224. MR 80g:55015

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E. Pedersen and C. Weibel, $K$-theory homology of spaces, Lecture Notes in Math., vol. 1370, Springer-Verlag, 1989, pp. 346-361. MR 90m:55007

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A. Suslin, Algebraic $K$-theory and Motivic Cohomology, Proc. International Congress of Mathematicians, Zürich 1994, vol. 1, Birkhäuser, 1995, pp. 342-351.

[T0]
R.W. Thomason, A note on spaces with normal product with some compact space, Proc. AMS 44 (1974), 509-510. MR 51:4165

[T-th]
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.

[T1]
R.W. Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), 91-109. MR 80b:18015

[T2]
R.W. Thomason, Uniqueness of delooping machines, Duke Math. J. 46 (1979), 217-252. MR 80e:55013

[T3]
R.W. Thomason, $\mathbf {Cat} $ as a closed model category, Cahiers Top. Geom. Diff. 21 (1980), 305-324. MR 82b:18005

[T4]
R.W. Thomason, First quadrant spectral sequences in algebraic $K$-theory, Lecture Notes in Math., vol. 763, Springer-Verlag, 1979, pp. 332-355. MR 81c:18018

[T5]
R.W. Thomason, First quadrant spectral sequences in algebraic $K$-theory via homotopy colimits, Comm. Algebra 10 (1982), 1589-1668. MR 83k:18006

[T6]
R.W. Thomason, Beware the phony multiplication on Quillen's $\mathcal {A}^{-1}\mathcal {A}$, Proc. AMS 80 (1980), 569-573. MR 81k:18010

[T-EC]
R.W. Thomason, Algebraic K-theory and étale cohomology, Ann. Scient. Éc. Norm. Sup. 18, $4^{e}$ série (1985), 437-552; erratum, vol. 22, 1989, pp. 675-677. MR 87k:14016; errata MR 91j:14013

[T7]
R.W. Thomason, The Lichtenbaum-Quillen conjecture for $K/\ell _{*}[\beta ^{-1}]$, Current Trends in Algebraic Topology, CMS Conf. Proc. vol. 2, Part 1, 1982, pp. 117-139. MR 84f:18024

[T8]
R.W. Thomason, Riemann-Roch for algebraic versus topological $K$-theory, J. Pure Appl. Alg 27 (1983), 87-109. MR 85c:14013

[T9]
R.W. Thomason, Bott stability in algebraic $K$-theory, AMS Contemp. Math., vol. 55, 1986, pp. 389-406. MR 87m:18022

[T10]
R.W. Thomason, The homotopy limit problem, AMS Contemp. Math., vol. 19, 1983, pp. 407-419. MR 84j:18012

[T11]
R.W. Thomason, Absolute cohomological purity, Bull. Soc. Math. France 112 (1984), 397-406. MR 87e:14018

[T12]
R.W. Thomason, Algebraic $K$-theory of group scheme actions, Annals of Math. Study 113 (1987), 539-563. MR 89c:18016

[T13]
R.W. Thomason, Lefschetz-Riemann-Roch theorem and coherent trace formula, Invent. Math. 85 (1986), 515-543. MR 87j:14028

[T14]
R.W. Thomason, Comparison of equivariant algebraic and topological $K$-theory, Duke Math. J. 53 (1986), 795-825. MR 88h:18011

[T15]
R.W. Thomason, Equivariant resolution, linearization and Hilbert's fourteenth problem over arbitrary base schemes, Adv. Math. 65 (1987), 16-34. MR 88g:14045

[T16]
R.W. Thomason, Equivariant algebraic vs. topological $K$-homology Atiyah-Segal-style, Duke Math. J. 56 (1988), 589-636. MR 89f:14015

[T17]
R.W. Thomason, The finite stable homotopy type of some topoi, J. Pure Appl. Alg. 47 (1987), 89-104. MR 88k:14010

[T18]
R.W. Thomason, A finiteness condition equivalent to the Tate conjecture over $\mathbb {F}_{q}$, AMS Contemp. Math., vol. 83, 1989, pp. 385-392. MR 90b:14029

[T19]
R.W. Thomason, Survey of algebraic vs. étale topological $K$-theory, AMS Contemp. Math., vol. 83, 1989, pp. 393-443. MR 90h:14029

[T20]
R.W. Thomason, The local to global principle in algebraic $K$-theory, Proc. International Congress of Mathematicians, Kyoto 1990, vol. 1, Springer-Verlag, 1991, pp. 381-394. MR 93e:19010

[T21]
R.W. Thomason, Une formule de Lefschetz en $K$-théorie équivariante algébrique, Duke Math. J. 68 (1992), 447-462. MR 93m:19007

[T22]
R.W. Thomason, Le principe de scindage et l'inexistence de $K$-théorie de Milnor globale, Topology 31 (1992), 571-588. MR 93j:19005

[T23]
R.W. Thomason, Les $K$-groupes d'un schéma éclaté et une formule d'intersection excédentaire, Invent. Math. 112 (1993), 195-215. MR 93k:19005

[T24]
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.

[T25]
R.W. Thomason, The classification of triangulated subcategories, preprint (1995), Compositio Math. (1996), to appear.

[T26]
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/).

[TT]
R.W. Thomason and T. Trobaugh, Higher algebraic $K$-theory of schemes and of derived categories, The Grothendieck Festschrift III, Progress in Math., vol. 88, Birkhäuser, 1990, pp. 247-435. MR 92f:19001

[TT1]
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[TW]
R.W. Thomason and S. Wilson, Hopf rings in the bar spectral sequence, Quart. J. Math Oxford 31 (1980), 507-511. MR 82f:55030

[Wald]
F. Waldhausen, Algebraic $K$-theory of spaces, Lecture Notes in Math., vol. 1126, Springer-Verlag, 1985, pp. 318-419. MR 86m:18011

[W]
C. Weibel, Robert W. Thomason (1952-1995), Notices of the AMS 43 (1996), 860-862.

[Y]
D. Yao, Higher algebraic $K$-theory of admissible abelian categories and localization theorems, Ph.D. thesis, Johns Hopkins University, Baltimore, 1990.

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Additional Information:

Charles A. Weibel
Affiliation: Mathematics Department, Rutgers University, New Brunswick, NJ 08903
Email: weibel@math.rutgers.edu

DOI: 10.1090/S0273-0979-97-00707-6
PII: S 0273-0979(97)00707-6
Received by editor(s): May 30, 1996
Additional Notes: Paper presented March 3, 1996, at The Fields Institute, Toronto
Author partially supported by NSF grant DMS95-00791.
Copyright of article: Copyright 1997, American Mathematical Society

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