Spencer Bloch Explained

Spencer Bloch
Birth Date:	22 May 1944
Birth Place:	New York City
Fields:	Mathematics
Workplaces:	University of Chicago
Alma Mater:	Harvard College Columbia University
Doctoral Advisor:	Steven Kleiman
Doctoral Students:	Caterina Consani Steven Zucker
Known For:	Bloch–Kato conjectures

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.

Awards and honors

Bloch is a member of the U.S. National Academy of Sciences^[6] and a Fellow of the American Academy of Arts and Sciences^{[7] [8]} and of the American Mathematical Society.^[9]

He received a Humboldt Prize in 1996.^[10] He also received a 2021 Leroy P. Steele Prize for Lifetime Achievement.^[11]

At the International Congress of Mathematicians, he gave an invited lecture in 1978^[12] and a plenary lecture in 1990.^{[8] [13]} He was a visiting scholar at the Institute for Advanced Study in 1981–82.^[14]

References

• James D. Lewis, and Rob de Jeu (Editors), Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch. Fields Institute Communications series, 2009, American Mathematical Society.

External links

• Spencer Bloch personal webpage, Department of Mathematics, University of Chicago

Notes and References

1. http://www.math.uchicago.edu/~bloch/cv Spencer Bloch CV
2. Book: Bloch, S. . Applications of the dilogarithm function in algebraic K-theory and algebraic geometry . Proc. Int. Symp. on Alg. Geometry . Nagata . M . Tokyo . Kinokuniya . 1978 . 103–114 .
3. Bloch . Spencer . Algebraic cycles and higher K-theory . . 61 . September 1986 . 267–304 . 10.1016/0001-8708(86)90081-2 . free.
4. [Daniel Quillen]
5. Bloch. Spencer. Kato. Kazuya. p-adic etale cohomology. Publications Mathématiques de l'IHÉS. 1986. 63. 107–152. 10.1007/bf02831624.
6. http://www.nasonline.org/site/Dir/522935353?pg=vprof&mbr=1001811&returl=http%3A%2F%2Fwww.nasonline.org%2Fsite%2FDir%2F522935353%3Fpg%3Dsrch%26view%3Dbasic&retmk=search_again_link Bloch, Spencer J.
7. http://www.amacad.org/enewsletter/a.pdf American Academy of Arts & Sciences, NEWLY ELECTED MEMBERS, APRIL 2009
8. http://chronicle.uchicago.edu/090430/aaas.shtml Scholars, visiting faculty, leaders represent Chicago as AAAS fellows
9. http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society
10. https://www.uchicago.edu/about/documents/provost/provost_report19951996.shtml Annual Report of the Provost, 1995–96
11. https://www.ams.org/news?news_id=6469 American Mathematical Society Announcement, November 19, 2020
12. Book: Bloch, S.. Algebraic K-theory and zeta functions of elliptic curves. In: Proceedings of the International Congress of Mathematicians (Helsinki, 1978). 511–515. 1978.
13. Book: Bloch, S.. Algebraic K-theory, motives, and algebraic cycles. 43–54. In: Proceedings of the International Congress of Mathematicians, August 21–29, 1990, Kyoto, Japan. 1991. Mathematical Society of Japan.
14. http://www.ias.edu/people/cos/ Institute for Advanced Study: A Community of Scholars