Representability of derived stacks. I would think that you would try to learn this stuff once it is clearly useful and interesting. The obtained moduli is too big as there are many isomorphic structures, so one needs to quotient by the automorphisms; this is a colimit type construction hence right exact. But if you only know “a few buzzwords”, I do not see how it could be interesting. SpringerVerlag, Berlin-New York,

Mac Lane homology and topological Hochschild homology. This came from the study of derived moduli problem. This might be and has been called 2-algebraic geometry. This definition is based on the observation that it is a deficiency of the ordinary definition of scheme to demand that underlying a scheme is a topological space and that a better definition is obtained by demanding it to have an underlying locale. Preprint Universitiit Bielefeld. How can I get to “research level mathematics”?

J, Lecture Notes in Math. Deformation quantization of algebraic varie ties. Nilpotence and Periodicity in Stable Homotopy Theor.

## Motives and derived algebraic geometry

Function complexes algebraiic homotopical algebra. Annals of Mathematics Studies, Unicorn Meta Zoo 3: Algebraic and geometric topology New Brunswick, N. To get some experience working with them, I would recommend reading some of the following papers:. On the co- homology of commutative rings.

See derived moduli stack of objects in a dg-category for details. On the homotopy of simplicial algebras over an operad. Proper local complete intersection morphisms preserve per fect complexes.

Toen, Derived Azumaya algebras and generators for twisted derived categoriesarXiv: How do we grade questions? This will make it a lot easier to understand what comes next. Rozansky-Witten invariants via Atiyah classes. The cotangent complex of a morphism.

This definition is based on the observation that it is a deficiency of the ordinary definition of scheme to demand that underlying a scheme is a topological space and that a better definition is obtained by demanding it to have an underlying locale. The irreducibility of the space of curves of given genus. The intrinsic normal cone. To get some experience working with them, I would recommend reading some of the following papers: Sometimes it may also refer to the subject of derived noncommutative algebraic geometry.

Simplicial localizations of categories.

# Derived Algebraic Geometry – INSPIRE-HEP

The local theory is basically understanding spectra stable stuffsimplicial rings and dg stuff. A big disadvantage to this method is that I don’t understand anything at a deep level and I’m only familiar with a few buzzwords. There are also these notes of Preygel. Globale Bruxelles, pp.

Towards higher categories,IMA Vol. Cambridge University Press, Cambridge, For this, read the first two chapters of the excellent lecture yhesis of Schapira. To appear in Crelles.

Mathematical Surveys and Monographs, Higher Segal spaces I. In Lurie, Structured spaces a definition of derived algebraic scheme? After that one should geimetry into a more specific topic. Galois extensions of structured ring spectra.

Press, Somerville, MA,