Math

This is a page of some mathematical things.

Grothendieck's Tohoku Paper

Grothendieck wrote "Sur quelques points d'algèbre homologique" in the Tohoku Math Journal, hence the moniker. Since I can't seem to obtain it from the usual FTP site, I mirrored it. Click here to download.

Books

These are math books that I have read a significant portion of and recommend highly:

• Weibel, An Introduction to Homological Algebra
• Kaplansky, Commutative Rings
• Conway, Functions of One Complex Variable
• Jacobson, Basic Algebra II

MathOverflow Questions

Some questions that I find interesting, or questions that have interesting answers. Note that question titles have been abridged because some of them are long.

Algebraic Geometry and Number Theory

1. General Stuff
• A learning roadmap for algebraic geometry
• Are there ever three perfect powers between consecutive squares?
• Grothendieck's Tohoku Paper and Combinatorial Topology
• "Algebraic" topologies like the Zariski topology?
• Grothendieck's Galois Theory today
2. Stacks
• Stacks of categories in algebraic geometry
• Stacks in the Zariski topology?
• In what topology DM stacks are stacks
• Stacks and sheaves
• What is a proper stack?
• Good introductory references on algebraic stacks?
3. Cohomology, Grothendieck Topologies, Etc.
• Etale cohomology - why study it?
• Varieties whose cohomology realizes certain representations
• comparison of de Rham cohomology and etale cohomology
• The etale fundamental group of a field
4. Modular and Automorphic Forms
• How is representation theory used in modular/automorphic forms?
• Definition of L-function attached to automorphic representation
• Is there a canonical notion of "mod-l automorphic representation"?
5. Miscellaneous
• When is a ring the ring of adeles of some global field
• Definition of L-function attached to automorphic representation
• Is there a canonical notion of "mod-l automorphic representation"?
• who fixed the topology on ideles?

Homological Algebra

1. General Stuff
• Ways of formulating homological algebra without diagram chasing
• Grothendieck spectral sequence and Mayer-Vietoris sequence
2. Spectral Sequences
• Simple examples for the use of spectral sequences
• What is so "spectral" about spectral sequences?
• Why are spectral sequences so ubiquitous?

General Algebra

1. Group Rings
• Zero divisor conjecture for finite fields