The cyclotomic trace and algebraic K -theory of spaces. Part 1, , Proc. Stably duali zable groups. Commutative algebras and cohomology. 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. I would question, however, why you have picked this subject if you do not have the requisite background. Higher Segal spaces I.
The tangent complex and Hochschild cohomology of E n -rings. Using dg-schemes , Ionut Ciocan-Fontanine and Mikhail Kapranov constructed the first derived moduli spaces derived Hilbert scheme and derived Quot scheme. Tannaka duality for geometric stacks. Gabriele Vezzosi , What is a derived stack? Preprint Universitiit Bielefeld. I would strongly recommend reading chapters 3 and 4 as well, but these can be skipped for now. DG-coalgebras as formal stacks
Tu the Lie algebroid of a derived self-intersection. 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 lurrie quotient by the automorphisms; this is a colimit type construction hence right exact. My goal is to study derived algebraic geometry, where derived schemes are built out of simplicial commutative rings rather than ordinary commutative rings as in algebraic geometry there’s also a variant using commutative ring spectra, which I don’t know anything about.
derived algebraic geometry in nLab
Anyways, since the category of simplicial rings form a model category, we can apply homotopy theoretic methods to study derived schemes.
In Lurie, Structured spaces a definition of derived algebraic scheme? HKR theorem for smooth S -algebras.
It may also be helpful to have a look at the first chapter of Lurie’s Higher algebra and the notes of Moritz Groth. Globale Bruxelles, pp. Preprint Universitiit Bielefeld.
Representability of derived stacks. Higher Segal spaces I.
Topological field theory, higher categories, and their appl ications. I would question, however, why you have picked this subject if you do not have the requisite background.
Motives and derived algebraic geometry
For references on dg-schemesthe historical precursor to derived schemessee there. On the variety of complexes.
Sign up or log in Sign up using Google. I propose the following plan, assuming a basic background in scheme theory and algebraic topology.
Algebraic geometric n -stacks.
soft question – Derived algebraic geometry: how to reach research level math? – MathOverflow
When is the self-intersection of a subvariety a fibration. New Mathematical Monographs, Lecture Notes in Mathematics, No. How can I get to “research level mathematics”? Proceedings of the International Congress of Mathematicians. J, Lecture Notes in Math. SpringerVerlag, Berlin-New York, Lecture Notes in Mathematics, Vol.
Using dg-schemesIonut Ciocan-Fontanine and Mikhail Kapranov constructed the first derived moduli spaces derived Hilbert scheme and derived Quot scheme. It will be helpful to consult sections of Cisinski’s Bourbaki talksection 40 of Joyal’s notes on quasi-categories, and Rezk’s notes. The tangent complex and Hochschild cohomology of E n -rings.