Semi-Infinite Algebraic Geometry of Quasi-Coherent Sheaves on Ind-Schemes

- 1. Ind-Schemes and Their Morphisms. - 2. Quasi-Coherent Torsion Sheaves. - 3. Flat Pro-Quasi-Coherent Pro-Sheaves. - 4. Dualizing Complexes on Ind-Noetherian Ind-Schemes. - 5. The Cotensor Product. - 6. Ind-Schemes of Ind-Finite Type and the factorial !-Tensor Product. - 7. X-Flat Pro-Quasi-Coherent Pro-Sheaves on Y. - 8. The Semitensor Product. - 9. Flat Affine Ind-Schemes over Ind-Schemes of Ind-Finite Type. - 10. Invariance Under Postcomposition with a Smooth Morphism. - 11. Some Infinite-Dimensional Geometric Examples.

Leonid Positselski did his undergraduate studies in Moscow in 1988-93 and received his Ph.D. in Mathematics from Harvard University in 1998. After a series of postdoctoral positions in the U.S. and Europe, he returned to Moscow in 2003. His first book was published in 2005 and the second one in 2010. In 2011-14 he taught as an Associate Professor at the Faculty of Mathematics of the Higher School of Economics in Moscow. Positselski emigrated from Russia to Israel in Spring 2014. Since 2018, he works as a researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.
Positselski is an algebraist specializing in Homological Algebra and homological aspects of various branches of the "algebraic half" of mathematics, including algebraic geometry, representation theory, commutative algebra, and algebraic K-theory.  He is known for his work on Koszul algebras and derived Koszul duality, as well as curved DG-rings, coderived and contraderived categories, and contramodules. Positselski penned more than 45 research papers and two survey papers. He is the author of five books and memoirs, including "Quadratic Algebras" (joint with A. Polishchuk, AMS University Lecture Series, 2005), "Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures" (Monografie Matematyczne IMPAN, Birkhäuser Basel, 2010), "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" (AMS Memoir, 2011), "Weakly curved A-infinity algebras over a topological local ring" (SMF Memoir, 2018-19), and "Relative nonhomogeneous Koszul duality" (Frontiers in Mathematics, Birkhäuser Switzerland, 2021-22).