Spencer Bloch

Spencer Bloch (2004)

Spencer Janney Bloch (born May 22, 1944 in New York ) is an American mathematician who deals with algebraic geometry and number theory.

life and work

Bloch studied at Harvard University until his bachelor's degree in 1966 and received his doctorate in 1971 from Columbia University with Steven Kleiman with the dissertation Algebraic Cohomology Classes on Algebraic Varieties . Then he was at Princeton University , from 1973 as an assistant professor. From 1974 to 1976 he was an associate professor at the University of Michigan and then at the University of Chicago , where he was professor from 1979 and has remained ever since, apart from visiting professorships in Cologne, Kyoto, Bonn, Cambridge and Paris. Today he is RM Hutchins Distinguished Service Professor Emeritus there.

Bloch was a Sloan Research Fellow (and later on its selection committee). He has been a member of the National Academy of Sciences since 1994 , of the American Academy of Arts and Sciences since 2009, and received the Humboldt Research Award in 1996 . He was invited speaker at the International Congress of Mathematicians (ICM) in Helsinki 1978 (Algebraic K-theory and zeta functions of elliptic curves) and Kyōto 1990 (plenary lecture: Algebraic K-theory, Motives and Algebraic Cycles). From 1982 to 1989 he was co-editor of the Bulletin of the American Mathematical Society and the American Journal of Mathematics. He is a fellow of the American Mathematical Society.

Bloch dealt with algebraic cycles , algebraic theory ${\ displaystyle K}$ and motifs . Higher Chow groups introduced by him provided candidates for the motivic theory of algebraic varieties over number fields assumed by Alexander Beilinson in 1982 . The Bloch- Kato conjectures make statements about the values of functions of projective algebraic varieties over number fields in integer places. The importance of analytic functions for obtaining information about the algebraic structure of number fields is shown in older sentences (such as Dirichlet's analytical class number formula ) and conjectures (such as the conjecture of Birch and Swinnerton-Dyer ), which are strongly generalized here. They refine the Beilinson conjecture from 1984. ${\ displaystyle K}$ ${\ displaystyle L}$ ${\ displaystyle L}$

His fundamental work Algebraic Cycles and Higher K-Theory from 1986 initially turned out to be flawed ( Andrei Suslin found an error in Lemma 1.1 soon after publication) and the error could only be corrected in 1993.

In the 1990s and 2000s he dealt, among other things, with algebro-geometric formulations of Chern-Simons theory and perturbation renormalization in quantum field theories .

Fonts

Higher regulators, K-theory and Zeta Functions of Elliptic Curves (Irvine Lectures from 1978), American Mathematical Society, Providence 2000
Lectures on algebraic cycles (Duke University 1979, published by Duke University 1980), Cambridge University Press 2010
K ₂ and algebraic cycles. Ann. of Math. (2) 99: 349-379 (1974).
with Ogus: Gersten's conjecture and the homology of schemes. Ann. Sci. École Norm. Sup. (4) 7 (1974): 181-201 (1975).
Algebraic K-theory and crystalline cohomology. Inst. Hautes Études Sci. Publ. Math. No. 1977, 47: 187-268 (1978).
Algebraic K-theory and classfield theory for arithmetic surfaces. Ann. of Math. (2) 114 (1981) no. 2, 229-265.
with Kato: p-adic étale cohomology. Inst. Hautes Études Sci. Publ. Math. No. 63 (1986), 107-152.
Algebraic cycles and higher K-theory. Adv. In Math. 61 (1986) no. 3, 267-304.
The moving lemma for higher chow groups. J. Algebraic Geom. 3 (1994) no. 3, 537-568.
with Esnault: A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory. Ann. of Math. (2) 151 (2000), no. 3, 1025-1070.
with Esnault, Kreimer: On motives associated to graph polynomials. Comm. Math. Phys. 267 (2006), no. 1, 181-225.
with Esnault, Kerz: p-adic deformation of algebraic cycle classes. Invent. Math. 195 (2014), no.3, 673-722.

literature

Rob de Jeu, James D. Lewis: Motives and algebraic cycles. A celebration in honor of Spencer J. Bloch , Fields Institute Communications, Fields Institute / American Mathematical Society, 2009

Web links

Web presence at the University of Chicago
Spencer Bloch in the Mathematics Genealogy Project (English)
Literature by and about Spencer Bloch in the catalog of the German National Library
Videos by and about Spencer Bloch in the AV portal of the Technical Information Library
Kings: The Bloch-Kato conjecture on special values of functions. A survey of known results. ${\ displaystyle L}$ Journal de Théorie des Nombres de Bordeaux, Volume 15 No. 1, pp. 179-198, 2003.

References

↑ Spencer Bloch: Algebraic cycles and higher theory . ${\ displaystyle K}$ Advances in Mathematics, Vol. 61, 1986, pp. 267-304.

^ Spencer Bloch, Kazuya Kato: Functions and Tamagawa numbers of motives. Grothendieck Festschrift Vol. 1, Birkhäuser, 1990, p. 333 ${\ displaystyle L}$

^ Voevodsky, The Origins and Motivations of Univalent Foundations, IAS 2014

personal data
SURNAME	Bloch, Spencer
ALTERNATIVE NAMES	Bloch, Spencer Janney (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	May 22, 1944
PLACE OF BIRTH	new York

[1] Spencer Bloch: Algebraic cycles and higher theory . ${\ displaystyle K}$ Advances in Mathematics, Vol. 61, 1986, pp. 267-304.