 His two-page note in the journal "Functional Analysis and Its Applications" was one of the papers on the study of derived categories of coherent sheaves.In 1981 Beilinson announced a proof of the Kazhdan–Lusztig conjectures and Jantzen conjectures with Joseph Bernstein.Independent of Beilinson and Bernstein, Brylinski and Kashiwara obtained a proof of the Kazhdan–Lusztig conjectures.