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, and 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.^[4]

Thomason's most influential work is a joint paper^[5] 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.^[6]

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, 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

References

1. Editorial Notice: Robert W. Thomason, 1952-1995
2. Robert Wayne Thomason at the Mathematics Genealogy Project
3. Weibel, Charles A. (1996), "Robert W. Thomason (1952–1995)" (PDF), Notices of the American Mathematical Society, 43 (8): 860–862, ISSN 0002-9920
4. O'Connor, John J.; Robertson, Edmund F., "Robert Wayne Thomason", MacTutor History of Mathematics Archive, University of St Andrews
5. Thomason, Robert W.; Trobaugh, Thomas (1990), "Higher Algebraic K-Theory of Schemes and of Derived Categories", The Grothendieck Festschrift Volume III, Progress in Mathematics, vol. 88, Boston, MA: Birkhäuser, pp. 247–435, doi:10.1007/978-0-8176-4576-2_10, ISBN 978-0-8176-3487-2, MR 1106918
6. 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

• Bak, Anthony; Weibel, Charles (1997), "A tribute to Robert Wayne Thomason (1952–1995)", K-Theory, 12 (1): 1–2, doi:10.1023/A:1007709906247, ISSN 0920-3036, MR 1466621
• Snaith, Victor (1997), "Robert Wayne Thomason. 1952–1995", Algebraic K-theory (Toronto, ON, 1996), Fields Institute Communications, vol. 16, Providence, R.I.: American Mathematical Society, pp. ix–xiii, MR 1466969
• Weibel, Charles A. (1997), "The mathematical enterprises of Robert Thomason", Bulletin of the American Mathematical Society, New Series, 34 (1): 1–13, doi:10.1090/S0273-0979-97-00707-6, ISSN 0002-9904, MR 1401423