2005/03/24 by Raphaël Rouquier, Raphael Rouquier, Rouquier, Raphael
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0503548
Bourbaki Seminar no 947, March 2005, in French
arxiv created 2005/03/24 · openalex publication_date 2005/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance and of minimization of the derived category have appeared, inspired by Kontsevich's homological mirror symmetry conjecture and Mori's minimal model program. We present the main conjectures and their proofs in dimension 3 and for particular classes of flops.