Vez zosi symplectic structures. Supplement this with section 2. On the De Rham cohomology of algebraic varieties. To appear in Crelles. For this, read the first two chapters of the excellent lecture notes of Schapira.
On the co- homology of commutative rings. This will make it a lot easier to understand what comes next. I would strongly recommend reading chapters 3 and 4 as well, but these can be skipped for now. On the homotopy of simplicial algebras over an operad. For a free resource, try ncatlab.
I would strongly recommend reading chapters 3 and 4 as well, but these can be skipped for now.
I would suggest, rather, naturally evolving from the things you already know well and find interesting. 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. In Lurie, Structured spaces a definition of derived algebraic scheme? To get some experience working with them, I would recommend reading some of the following papers:. Loop spaces and connections.
On the homotopy of simplicial algebras over an operad.
Derived Algebraic Geometry – INSPIRE-HEP
Globale Bruxelles, pp.
soft question – Derived algebraic geometry: how to reach research level math? – MathOverflow
Differential Graded Schemes II: How should I study this book? Completions and derived de Rham cohomology. Press, Somerville, MA, If you are interested in applications to topology, you should replace part 2 of the plan by Lurie’s Higher algebra.
It will be helpful to consult sections of Cisinski’s Bourbaki talksection 40 of Joyal’s notes on quasi-categories, and Rezk’s notes.
Proceedings of the International Congress of Mathematicians. Tangent Lie algebra of derived Artin stacks.
Motives and derived algebraic geometry
Formality of derived intersections, preprint. This is effectively the perspective on noncommutative algebraic geometry that Maxim Kontsevich has been promoting.
Deformation quantization of algebraic varie ties. Home Questions Tags Users Unanswered. Locally complete intersection homomorphisms and a conject ure of Quillen on the vanishing of cotangent homology. The 2-category of Differenti al Luroe Schemes. Preprint Universitiit Bielefeld.
Enumeration of rational curves via torus actions. You might find in the beginning some proofs which involve technical combinatorics of simplices. I would think that you would try to learn this stuff once it is clearly useful and interesting.
See also Gaitsgory’s notes he works with commutative connective dg-algebras instead of simplicial commutative rings, but this makes little difference. Other helpful things to look at are Schwede’s Diplomarbeit and Quillen’s Homology of commutative rings. Calculus of fractions and homotopy theory. The tangent complex and Hochschild cohomology of E n thwsis.