J , , Lecture Notes in Math. To appear in Crelles. Sometimes it may also refer to the subject of derived noncommutative algebraic geometry. This came from the study of derived moduli problem. Topol 5 , no.
Tangent Lie algebra of derived Artin stacks. And none of these topics is contained in HTT.
Motives and derived algebraic geometry
There are also these notes of Preygel. Then read chapters I and II of Gabriel-Zisman, Calculus of fractions and homotopy theoryto learn about the theory of localization of categories. Jones’ theoremDeligne-Kontsevich conjecture. Moduli problems for ring spectra.
The plan is based on what worked best for myself, and it’s certainly possible that you may prefer to jump into Higher Topos Theory as Yonatan suggested. Then you could look at this mathoverflow.
Towards higher categories,IMA Vol. Topol 5no. On the Gauss-Manin connection in cyclic homology.
I thought the first thing I should do is study simplicial homotopy theory, in order geometfy learn about model categories and simplicial objects. Mac Lane homology and topological Hochschild homology. The local theory is basically understanding spectra stable stuffsimplicial rings and dg stuff.
The Geometry of the master equation and topological quantum field theory – Alexandrov, M. Thess as formal stacks I recommend working through Cisinski’s notes.
Derived Algebraic Geometry – INSPIRE-HEP
Virtual fundamental classes via dg-manifolds. The following notes deal with the theory modelled on coconnective commutative dg-algebras. By the way, these ones are in English and also summarize very briefly some of the material from the longer course notes.
Motives and derived algebraic geometry – Essen, May
Operads and motives in deformation quantization. The relation between noncommutative algebraic geometry and derived algebraic geometry may then be summed up by the adjunction.
New Mathematical Monographs, Satisfying these equations is a limit-type construction, hence left exact and one is lead to right derived functors to improve; exactness on the right; this leads to use cochain complexes. Hodge theoretic aspects of mirror symmetry. Supplement this with section 2.
dwrived Bertrand Toen and Gabriele Vezzosi developed homotopical algebraic geometrywhich is algebraic geometry in any HAG contexti. The cyclotomic trace and algebraic K -theory of spaces. The irreducibility of the space of curves of given genus.
On the co- homology of commutative rings. Mathematical Surveys and Monographs, After that one should delve into a more specific topic.