Robert Wayne Thomason

Robert Wayne Thomason (5 November 1952 – 5 November 1995)^[1] was an American mathematician who worked on algebraic K-theory. His results include a proof that all infinite loop space machines are in some sense equivalent, and progress on the Quillen–Lichtenbaum conjecture.

Robert Wayne Thomason
Born	(1952-11-05)November 5, 1952 Tulsa, Oklahoma, United States
Died	November 5, 1995(1995-11-05) (aged 43) Paris, France
Alma mater	Michigan State University Princeton University
Known for	Work on algebraic K-theory
Scientific career
Fields	Mathematics
Institutions	Massachusetts Institute of Technology University of Chicago Johns Hopkins University
Thesis	Homotopy Colimits in Cat(+ Category of Small Categories) with Applications to Algebraic K-Theory and Loop Space Theory (1977)
Doctoral advisor	John Coleman Moore

Born in Tulsa, Oklahoma, Thomason did his undergraduate studies at Michigan State University, graduating with a B.S. in mathematics in 1973. He completed his Ph.D. at Princeton University in 1977, under the supervision of John Moore.^[2] According to Charles Weibel,^[3] Thomason proved the equivalence of all infinite loop space machines in June 1977. He was just a 24 years old graduate student at the time; he published this result the year after in a joint paper with John Peter May.

From 1977 to 1979 he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology, where he wrote his article ^[4] showing that the category Cat of small categories has a structure of Quillen model category that is Quillen-equivalent to the categories of simplicial sets and topological spaces. From 1979 to 1980 he was a Dickson Assistant Professor at the University of Chicago before resigning due to "perceived persecution" by senior faculty.^[3] After spending a year as a lecturer at MIT and another at the Institute for Advanced Study, he was appointed as faculty at Johns Hopkins University in 1983. While there, he was awarded a Sloan Research Fellowship, which allowed him to spend the year 1987 at Rutgers University.^[5]

Thomason's most influential work is a joint paper^[6] with Thomas Trobaugh, even though Trobaugh had died by the time this paper was written. According to Weibel,^[3] "On January 22, 1988, [Thomason] had a dream in which Thomas Trobaugh, who had passed away recently, told him how to solve the [most difficult] final step. [..] In gratitude [Thomason] listed his friend as a coauthor of the resulting paper." Among the many results of this paper are construction of the K-theory spectrum for the category of perfect complexes of coherent sheaves on a scheme, and the proof for localization theorems in algebraic K-theory which include the case of non-regular schemes (Theorem 2.1). Thomason also proved Mayer–Vietoris-type theorem for algebraic K-theory of schemes. Following the publication of his paper with Trobaugh, Thomason was invited to give an invited talk at the 1990 International Congress of Mathematicians in Kyoto.^[7] From October 1989, Thomason held a position in Max Karoubi's laboratory at the University of Paris VII.^[8]

Thomason suffered from diabetes; in early November 1995, just shy of his 43rd birthday, he went into diabetic shock and died in his apartment in Paris.^[3]

Publications

• May, J. Peter; Thomason, R. (1978), "The uniqueness of infinite loop space machines", Topology, 17 (3): 205–224, doi:10.1016/0040-9383(78)90026-5, ISSN 0040-9383, MR 0508885
• Thomason, R. W. (1980), "Cat as a closed model category", Cahiers de Topologie et Géométrie Différentielle Catégoriques, 21 (3): 305–324, ISSN 1245-530X, MR 0591388
• Thomason, Robert W. (1985), "Algebraic K-theory and étale cohomology" (PDF), Annales Scientifiques de l'École Normale Supérieure, Quatrième Série, 18 (3): 437–552, doi:10.24033/asens.1495, ISSN 0012-9593, MR 0826102 Erratum
• Thomason, Robert W.; Trobaugh, Thomas (1990), "Higher Algebraic K-Theory of Schemes and of Derived Categories", The Grothendieck Festschrift Volume III, Progr. Math., vol. 88, Boston, MA: Birkhäuser Boston, pp. 247–435, doi:10.1007/978-0-8176-4576-2_10, ISBN 978-0-8176-3487-2, MR 1106918
• Thomason, Robert W. (1991), "The local to global principle in algebraic K-theory", in Satake, Ichirô (ed.), Proceedings of the International Congress of Mathematicians, Vol. I (Kyoto, 1990), Tokyo: Math. Soc. Japan, pp. 381–394, ISBN 978-4-431-70047-0, MR 1159226