What Is... Seminar
Derived schemes are basic geometric objects (`spaces') studied in derived algebraic geometry, a relatively new area of mathematics that stands at the crossroads of algebraic geometry and algebraic topology (homotopy theory). Just as a classical algebraic variety (or scheme) is locally modeled on commutative rings, a derived scheme is modeled on simplicial or differential graded commutative rings, which are homotopical versions of commutative rings. In this talk, I will explain what derived schemes (and more generally, derived stacks) are and what they can be useful for. I will try to provide motivation from the both sides: algebraic geometry and topology.