# nLab Joseph Bernstein

Selected writings

Joseph Bernstein is an Israeli mathematician, born and educated in Russia (his Russian name iss Иосиф Наумович Бернштейн, transliterated as Josif/Iosif Naumovič Bernštejn); his teacher there was Israel Gel'fand. His numerous works (especically with Alexander Beilinson) brought to proliferation of sheaf-theoretic and algebro-geometric methods in representation theory (D-modules, perverse sheaves, Beilinson-Bernstein localization theory), and are now cornerstones of geometric representation theory. With V. Lunts he introduced the appropriate definition of equivariant derived category (in general not equivalent to the (naive) derived category of equivariant sheaves).

## Selected writings

• I. N. Bernšteĭn, I. M. Gelʹfand, V. A. Ponomarev, Coxeter functors, and Gabriel’s theorem. (Russian) Uspehi Mat. Nauk 28 (1973), no. 2(170), 19–33.

• J. N. Bernstein, I. M. Gel’fand, S. I. Gel’fand, Алгебраические расслоения на $P^n$ и задачи линейной алгебры, Функц. анализ и его прил., 12:3 (1978), 66–67, pdf (Russian); Engl. transl. Algebraic bundles over $P^n$ and problems of linear algebra, Funct. Anal. and its Appl. 1978, 12:3, 212–214

• A. Beilinson, J. Bernstein, Localisations de $\mathfrak{g}$–modules, C. R. Acad. Sci. Paris 292 (1981), 15–18.

• A. A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, Astérisque 100 (1983).

• J. Bernstein, V. Lunts, On nonholonomic irreducible D-modules, Invent. Math. 94)), (1988), no. 2, 223–243.

• J. Bernstein, V. Lunts, Equivariant sheaves and functors, Springer Lecture Notes in Math. 1578 (1994). MR95k:55012

• A. Beĭlinson, J. Bernstein, A proof of Jantzen conjectures, I. M. Gelʹfand Seminar, 1–50, Adv. Soviet Math. 16, Part 1, Amer. Math. Soc. 1993, pdf

• Joseph Bernstein’s notes on D-modules: pdf

On the Langlands program:

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