Holmstrom Derived algebraic geometry

Jacob Lurie’s thesis

http://mathoverflow.net/questions/37825/what-are-jacob-luries-key-insights

http://mathoverflow.net/questions/15687/what-is-dag-and-what-has-it-to-do-with-the-ideas-of-voevodsky

See Toen: Essen talk, for intro to his ideas, including refs to dg schemes, and a reasonable amount of substance on derived moduli stacks towards the end.

http://mathoverflow.net/questions/55053/complicating-an-example-by-toen-motivations-for-dag

An excellent introduction to derived AG is the CRM 2008 notes, in Toen web unpublished folder. These notes also covers algebraic stacks, the idea of moduli spaces, a little about cotangent complexes, and examples of derived algebraic stacks.

Resources by Akhil M

nlab on derived noncomm geom

nlab on DAG

http://mathoverflow.net/questions/54591/does-derived-algebraic-geometry-allow-us-to-take-quotients-with-reckless-abandon

http://mathoverflow.net/questions/30396/derived-algebraic-geometry-and-chow-rings-chow-motives

arXiv:1208.6325 Grothendieck-Riemann-Roch for derived schemes from arXiv Front: math.AG by Parker Lowrey, Timo Schürg We define bivariant algebraic K-theory and bivariant derived Chow on the homotopy category of derived schemes over a smooth base. The orientation on the latter corresponds to virtual Gysin homomorphisms. We then provide a morphism between these two bivariant theories and compare the two orientations. This comparison then yields a homological and cohomological Grothendieck-Riemann-Roch formula for virtual classes.

nLab page on Derived algebraic geometry