Holmstrom Motivic homotopy theory reading

This is a list useful reading on homotopy theory in algebraic geometry. For a lot more resources, see the resource page maintained by Aravind Asok

Background in Algebraic Geometry

Summary of background in algebraic geometry: notes by Marc Levine.

Many useful notes, including an introduction to sheaf cohomology, can be found at The Rising Sea

Background in Category Theory

Basic category theory

Additive and abelian categories

Notes by Fesenko.

Triangulated categories

Notes by Henning Krause.

Model categories

A very readable introduction by Dwyer and Spalinski.

Higher categories

A guide by Cheng and Lauda.

Background in Algebraic Topology

The excellent book by May should cover everything.

A nice background paper by Dundas

Some slides by Strickland on stable homotopy

See reading list on page 2 of Strickland’s bestiary

Unstable homotopy theory

DEA thesis by Joel Riou.

The original paper by Morel and Voevodsky

Stable homotopy theory

Notes from Tyler Lawson’s page

Voevodsky’s ICM lecture

Gillet in K-theory handbook, section 2.5.

Many nice things are in these notes by Dundas. More generally, check the Nordfjordeid summer school volume on motivic homotopy theory. Available in folder AG/Motives.

Talk in Toronto by Levine

See lectures of Levine at the Asian-French summer school

Voevodsky: Open problems I

Slides of Jardine

Levine: The homotopy coniveau filtration. (Looks very nice) See also Chow’s moving lemma and the homotopy coniveau tower.

Check all other papers of Voevodsky!

Weibel’s road map

Hornbostel on motivic chromatic homotopy theory.

Po Hu on the Picard group, and on S-modules in the stable homotopy category of schemes. Here is also something on the Steinberg relation

Check the paper on Motivic functors by Bjørn Ian Dundas, Oliver Röndigs, Paul Arne Østvær.

Motivic cell structures , by Daniel Dugger and Daniel C. Isaksen

Levine slides on Postnikov towers. See by the way everything on Levine’s web page, for example this

Biedermann: L-stable functors. “This gives a particularly easy construction of the classical and the motivic stable homotopy category with the correct smash product.”

Weight structures, weight filtrations, weight spectral sequences, and weight complexes (for motives and spectra) , by Mikhail V. Bondarko: http://www.math.uiuc.edu/K-theory/0843

Joseph Ayoub thesis, on the six operations formalism in the stable homotopy category. Also: Ayoub in Nagel and Peters: nice exposition of various categories.

Opérations sur la K-théorie algébrique et régulateurs via la théorie homotopique des schémas, by Joël Riou

Severitt

Half-page intro by Grayson, K-th handbook p 63.

Short intro by Kahn in K-theory handbook, pp374 (a possible starting point for rewriting stuff).

Some abstrast/axiomatic views on stable homotopy

Joel Riou on the stable homotopy category of a site with interval. See also http://www.math.uiuc.edu/K-theory/0825

Interesting mathematicians

Levine Toen Jardine Morel Voevedsky Kahn

Ideas/questions

Can one work with infinite loop space machines in algebraic geometry? Can this lead to a recognition principle?

Some Open questions - a summary from a conference in Palo Alto

nLab page on Motivic homotopy theory reading

Created on June 9, 2014 at 21:16:13 by Andreas Holmström