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Arithmeticity theorem — Grigory Margulis

1974 AD · Transmission: Disputed
MathematicsTheoryRussian

Grigory Margulis proves in 1974, announcing it at the International Congress of Mathematicians in Vancouver and publishing it over the following years, the arithmeticity theorem: every irreducible lattice in a semisimple Lie group of rank greater than 1 is arithmetic, that is, it can be obtained via an explicit algebraic construction analogous to taking matrices with integer coefficients. The result proves a conjecture formulated by Atle Selberg — also a Fields laureate, in 1950 — and decisively employs methods from ergodic theory applied to a problem of algebraic nature, opening a line of research that would remain active for decades. Margulis received the Fields Medal in 1978, but the Soviet government did not allow him to travel to Helsinki to collect it in person.

InstitutionInstitute of Problems of Information Transmission, Moscow
Historical regionUSSR
Primary sourceMargulis, G. A. — "Arithmetic properties of discrete subgroups" (Uspekhi Matematicheskikh Nauk, 29, 1974); "Discrete groups of motions of manifolds of nonpositive curvature" (Proceedings of the ICM Vancouver, 1974/1975)
Secondary sourceInternational Mathematical Union — Fields Medal citation 1978
Original languageRussian
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