The local theory is basically understanding spectra stable stuff , simplicial rings and dg stuff. Derived completions in stable homotopy theory. Press, Somerville, MA, SpringerVerlag, Berlin-New York, In addition, the book also contains appendices which explain classical material such as model categories in a very readable way. Apr 27 ’18 at
Cambridge University Press, Cambridge, Together with these ones you can try Lurie’s thesis however it has few proofs. The irreducibility of the space of curves of given genus. Proper local complete intersection morphisms preserve per fect complexes. I would think that you would try to learn this stuff once it is clearly useful and interesting. Eventually, pieces falls into places. Other helpful things to look at are Schwede’s Diplomarbeit and Quillen’s Homology of commutative rings.
Motives and derived algebraic geometry
The 2-category of Differenti al Graded Schemes. Triviality of the higher Formality Theorem.
I’m a senior math major and I’ve taken the graduate algebraic geometry and algebraic topology sequences. HKR theorem for smooth S -algebras. In addition, the book also contains appendices which explain classical material such as model categories in a very readable way. Topological field deived, higher categories, and their appl ications.
Please direct questions, comments or concerns to feedback inspirehep. Virtual fundamental classes via dg-manifolds. Jacob LurieDerived Algebraic Geometry.
In this fashion then in derived noncommutative algebraic geometrya space is by definition a dg-category that is smooth and proper in an appropriate sense. Towards higher categories,IMA Vol.
derived algebraic geometry in nLab
Algebraic aspects of higher nonabelian Hodge theory. The local theory is basically understanding spectra stable stuffsimplicial rings and dg stuff. Proper local complete intersection morphisms preserve per fect complexes. If you are interested in applications to topology, you should replace part 2 of the plan by Lurie’s Higher algebra. Lecture Notes in Mathematics, No.
DG-coalgebras as formal stacks The cotangent complex of a morphism. Rozansky-Witten invariants via Atiyah classes. The proofs in the book do become increasingly conceptual with each chapter, as the concepts themselves get built and acquire depth.
The cyclotomic trace and algebraic K -theory of spaces. The relation between noncommutative algebraic alggebraic and derived algebraic geometry may then be summed up by the adjunction.
Moduli problems for ring spectra. This site is also available in the following languages: Sometimes the term derived algebraic geometry is also used for the related subject of spectral algebraic geometrywhere commutative ring spectra are used instead of algebraiic commutative rings.
Derived Algebraic Geometry – INSPIRE-HEP
SpringerVerlag, Berlin-New York, Topological modular forms [after Hopkins, Miller and Lurie]. Equivalences of monoidal model categories. Versal deformations and algebraic stacks. The thesie 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.
The deformation theory of representations of fundamental g roups of compact Khler manifolds.