By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Nilpotence and stable homotopy theory. To get some experience working with them, I would recommend reading some of the following papers:. I recommend working through Cisinski’s notes. Moduli problems for ring spectra.

MathOverflow works best with JavaScript enabled. Apr 27 ’18 at The proofs in the book do become increasingly conceptual with each chapter, as the concepts themselves get built and acquire depth. Jones’ theorem , Deligne-Kontsevich conjecture. Locally complete intersection homomorphisms and a conject ure of Quillen on the vanishing of cotangent homology. 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. The cyclotomic trace and algebraic K -theory of spaces.

Sm ith limit functors on model categories and homotopical categories.

I know the question “how to study math” has been asked dozens of times before in many variations, but I hope this one is different. Globale Bruxelles, pp.

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. Operads and motives in deformation quantization. Following that, if you have a book without exercises, you need to make your own, and ideally you should be talking with other people about the content. Sign up or log in Sign up using Google.

## Motives and derived algebraic geometry

Tangent Lie algebra of derived Artin stacks. Galois extensions of structured ring spectra.

Higher and derived stacks: I’m a senior math major and I’ve taken the graduate algebraic geometry and algebraic topology sequences. Algebraic aspects of higher nonabelian Hodge theory. Feeling comfortable with simplices is essential and this requires working out some details. Tannaka duality for geometric stacks. The tangent complex and Hochschild thesiz of E n -rings.

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# soft question – Derived algebraic geometry: how to reach research level math? – MathOverflow

Cartesian presentation of weak n -categories. The hidden smoothness principle of Maxim Kontsevichwhich conjectures that in classical algebraic geometrythe non- smoothness?

These notes are very brief, so you will have to algwbraic them with the notes of Joyal. Sometimes the term derived algebraic geometry is also used for the related subject of spectral algebraic geometrywhere commutative ring spectra are used instead of simplicial commutative rings. But a locale is a 0-topos.

This material is at the heart of derived algebraic geometry: How do we grade questions? Enumeration of rational curves via torus actions. The Lie algebra structure of tangent cohomology and deforma tion theory DG-coalgebras as formal stacks Representability of derived stacks. Proceedings of the International Congress of Mathematicians. This might be and has been called 2-algebraic geometry.

# derived algebraic geometry in nLab

On differential graded categories. So what should I do?

Descente pour les n-champs Descent for n-stacks. The following notes deal with the theory modelled on E-infinity ring spectra E-infinity geometry:.

Deformation quantization of algebraic varie ties. How can I get to “research level mathematics”?