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Spencer Bloch
Spencer Bloch
	Bloch at Oberwolfach in 2004
Born	May 22, 1944 (age 80); New York City
Alma mater	Harvard College; Columbia University
Known for	Bloch–Kato conjectures
	Scientific career
Fields	Mathematics
Institutions	University of Chicago
Doctoral advisor	Steven Kleiman
Doctoral students	Caterina Consani; Steven Zucker;

Spencer Janney Bloch (born May 22, 1944; New York City^[1]) is an American mathematician known for his contributions to algebraic geometry and algebraic K-theory. Bloch is a R. M. Hutchins Distinguished Service Professor Emeritus in the Department of Mathematics of the University of Chicago.

Research

Bloch introduced the Bloch group in 1978.^[2] He introduced Bloch's higher Chow group, a generalization of Chow groups, in 1986.^[3] He also introduced Bloch's formula in Algebraic K-theory.^[4]

Bloch and Kazuya Kato formulated the motivic Bloch–Kato conjecture relating Milnor K-theory and Galois cohomology in 1986^[5] and the Bloch–Kato conjectures for special values of L-functions in 1990.^[6]

Awards and honors

Bloch is a member of the U.S. National Academy of Sciences^[7] and a Fellow of the American Academy of Arts and Sciences^[8]^[9] and of the American Mathematical Society.^[10]

He received a Humboldt Prize in 1996.^[11] He also received a 2021 Leroy P. Steele Prize for Lifetime Achievement.^[12]

At the International Congress of Mathematicians, he gave an invited lecture in 1978^[13] and a plenary lecture in 1990.^[9]^[14] He was a visiting scholar at the Institute for Advanced Study in 1981–82.^[15]

References

^ Spencer Bloch CV, Department of Mathematics, University of Chicago. Accessed January 12, 2010
^ Bloch, S. (1978). "Applications of the dilogarithm function in algebraic K-theory and algebraic geometry". In Nagata, M (ed.). Proc. Int. Symp. on Alg. Geometry. Tokyo: Kinokuniya. pp. 103–114.
^ Bloch, Spencer (September 1986). "Algebraic cycles and higher K-theory". Advances in Mathematics. 61 (3): 267–304. doi:10.1016/0001-8708(86)90081-2.
^ Daniel Quillen: Higher algebraic K-theory: I. In: H. Bass (ed.): Higher K-Theories. Lecture Notes in Mathematics, vol. 341. Springer-Verlag, Berlin 1973. ISBN 3-540-06434-6
^ Bloch, Spencer; Kato, Kazuya (1986). "p-adic etale cohomology". Publications Mathématiques de l'IHÉS. 63: 107–152. doi:10.1007/bf02831624.
^ Kings, Guido (2003), "The Bloch–Kato conjecture on special values of L-functions. A survey of known results", Journal de théorie des nombres de Bordeaux, 15 (1): 179–198, doi:10.5802/jtnb.396, ISSN 1246-7405, MR 2019010
^ Bloch, Spencer J. U.S. National Academy of Sciences. Accessed January 12, 2010. Election Citation: "Bloch has done pioneering work in the application of higher algebraic K-theory to algebraic geometry, particularly in problems related to algebraic cycles, and is regarded as the world's leader in this field. His work has firmly established higher K-theory as a fundamental tool in algebraic geometry."
^ American Academy of Arts & Sciences, NEWLY ELECTED MEMBERS, APRIL 2009 Archived August 8, 2013, at the Wayback Machine, American Academy of Arts and Sciences. Accessed January 12, 2010
^ ^a ^b Scholars, visiting faculty, leaders represent Chicago as AAAS fellows, The University of Chicago Chronicle, April 30, 2009, Vol. 28 No. 15. Accessed January 12, 2010
^ List of Fellows of the American Mathematical Society, retrieved November 10, 2012.
^ Annual Report of the Provost, 1995–96, University of Chicago. Accessed January 12, 2010.
^ American Mathematical Society Announcement, November 19, 2020. Accessed November 25, 2020.
^ Bloch, S. (1978). "Algebraic K-theory and zeta functions of elliptic curves". In: Proceedings of the International Congress of Mathematicians (Helsinki, 1978). pp. 511–515.
^ Bloch, S. (1991). "Algebraic K-theory, motives, and algebraic cycles". In: Proceedings of the International Congress of Mathematicians, August 21–29, 1990, Kyoto, Japan. Mathematical Society of Japan. pp. 43–54.
^ Institute for Advanced Study: A Community of Scholars