Mikhail Borovoi
Mikhail Vol'fovich Borovoi (Russian: Михаи́л Во́льфович Борово́й, Hebrew: מיכאל בורובוי, born February 17, 1951) is a Soviet and Israeli mathematician. He has worked on Galois cohomology and on the arithmetic of linear algebraic groups, homogeneous spaces, Shimura varieties, and spherical varieties.
Education and career[edit]
Borovoi was born in Moscow. He obtained his diploma (M.Sc.) in Mathematics at Lomonosov Moscow State University, and his Ph.D. at the Leningrad Department (now: St. Petersburg Department) of the Steklov Institute of Mathematics[1] in 1980; his doctoral advisor was Arkady L. Onishchik. Because of Antisemitism in the Soviet Union of the time, Borovoi could not find a job as a mathematician, and only with the start of Perestroika, in 1987 he got a position of a Senior Researcher at the Khabarovsk Division of the Institute for Applied Mathematics of the Far Eastern Branch of the USSR Academy of Sciences[2] in the Far Eastern city of Khabarovsk. He spent the 1990-1991 academic year at the Institute for Advanced Study.[2] Since 1992 he has been at Tel Aviv University,[2] where now he is Professor Emeritus.[3]
Research[edit]
Borovoi is known for the Borovoi fundamental group[4] of a reductive group. Jointly with James S. Milne,[5] Borovoi proved[6] Shimura's conjecture in the theory of Shimura varieties, which was the subject of Borovoi's invited talk[7] at the International Congress of Mathematicians, Berkeley, 1986. He proved that the Brauer-Manin obstruction is the only obstruction to the Hasse principle and weak approximation for homogeneous spaces of connected linear algebraic groups over number fields with connected geometric stabilizers.[8] Jointly with Cyril Demarche, he proved a similar result for the Brauer-Manin obstruction to strong approximation[9]
References[edit]
- ^ Mikhail Borovoi at the Mathematics Genealogy Project
- ^ a b c Page of Mikhail Borovoi in the List of Scholars of the Institute for Advanced Study
- ^ List of Professors Emeriti of the School of Mathematical Sciences, Tel Aviv University
- ^ Laurent Fargues and Peter Scholze, Geometrization of the local Langlands correspondence, https://arxiv.org/abs/2102.13459, p. 90
- ^ James S. Milne, The action of an automorphism of C on a Shimura variety and its special points. Arithmetic and Geometry, Vol. I, 239-265, Progr. Math., 35, Birkhäuser Boston, Boston, MA, 1983.
- ^ M. V. Borovoi, Langlands' conjecture concerning conjugation of connected Shimura varieties. Selecta Math. Soviet. 3 (1983/84), no. 1, 3–39.
- ^ M. V. Borovoi, Conjugation of Shimura varieties. Proceedings of the International Congress of Mathematicians, Vol. 1 (Berkeley, Calif.,1986), 783-790, Amer. Math. Soc., Providence, RI, 1987.
- ^ Mikhail Borovoi, The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer. J. Reine Angew. Math. 473 (1996), 181-194, DOI: https://doi.org/10.1515/crll.1995.473.181.
- ^ Mikhail Borovoi and Cyril Demarche, Manin obstruction to strong approximation for homogeneous spaces. Comment. Math. Helv. 88 (2013), no. 1, 1-54, DOI: https://doi.org/10.4171/CMH/277.