George Khachatryan

Ph.D. (2011) Cornell University

algebraic geometry, homological algebra, and representation theory

After surveying relevant literature (on representation schemes, homotopical algebra, and non-commutative algebraic geometry), we provide a simple algebraic construction of relative derived representation schemes and prove that it constitutes a derived functor in the sense of Quillen. Using this construction, we introduce a derived Kontsevich-Rosenberg principle. We also prove a theorem allowing one to finitely present derived representation schemes of an associative algebra whenever one has an explicit finite presentation for an almost free resolution of that algebra; using this theorem, we calculate several examples.