Oeuvres - Collected Papers IV

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The impact of J.-P. Serre's work has been significant since his doctoral thesis on homotopy groups. His research spans various fields, including topology, complex variables, algebraic geometry, number theory, group theory, commutative algebra, and modular forms, providing valuable insights for mathematicians in research and teaching. Serre's publications often present open questions that guide future research directions. In the four volumes of his Collected Papers, he includes comments and corrections for most articles, detailing the status of open questions in light of later findings. This softcover edition of volume IV features two new articles: one on André Weil's life and works, and another on Finite Subgroups of Lie Groups. This volume covers Serre's work from 1985-1998, with items numbered 133-173 focusing on number theory, algebraic geometry, and group theory. It includes both articles and summaries of his unpublished courses, alongside letters that hint at proofs for announced results. An interview from 1986 offers insight into Serre's mathematical philosophy, emphasizing integrity and his own research. The volume concludes with Notes that provide updates and corrections to the text.