Video library: Alexey Elagin, Atomic theory for the derived categories of surfaces

VIDEO LIBRARY


Workshop on birational geometry December 11, 2025 12:30, Moscow, Steklov Mathematical Institute, online

Atomic theory for the derived categories of surfaces Alexey Elagin The University of Sheffield
Abstract: There is an old idea that birational geometry (in particular, the Minimal Model Program) can and should be translated into the language of derived categories. We revive this idea by constructing “atomic” semi-orthogonal decompositions of derived categories of smooth algebraic surfaces, over any perfect field or in $G$-equivariant setting. “Atoms” of these decompositions provide birational invariants of surfaces, similar to invariants studied by Lin–Shinder–Zimmermann and Auel–Bernardara. After constructing “atomic” theory, I will explain the role that “atoms” can play in the classification of geometrically rational surfaces over non-closed fields. This is a joint work with Evgeny Shinder and Julia Schneider, and the idea goes back to Kontsevich and quantum cohomology. Language: English