I’ll be spending the academic year 2012-13 at UCLA, and so leaving one well-stocked university library for another. Nevertheless, like every mathematician, I have some favorite books — for research, teaching, and finishing my book — that I can’t be without. After a lot of fussing, in an effort to pack light, I’ve chosen a core traveling library to take from Cambridge to Los Angeles:

Adem/Milgram, *Cohomology of finite groups*

Atiyah/Macdonald, *Introduction to commutative algebra*

Benson, *Representations and cohomology, I and II*

Benson, *Polynomial invariants of finite groups*

Bloch, *Lectures on algebraic cyc*les

Brown, *Cohomology of groups*

Eisenbud, *Commutative algebra with a view toward algebraic geometry*

Fulton, *Intersection theory*

Fulton, *Introduction to toric varieties*

Fulton/Harris, *Representation theory*

Garibaldi/Merkurjev/Serre, *Cohomological invariants of algebraic groups*

Griffiths/Harris, *Principles of algebraic geometry*

Hartshorne, *Algebraic geometry*

Kobayashi, *Hyperbolic manifolds and holomorphic mappings*

Kollár, *Lectures on resolution of singularities*

Kollár, *Shafarevich maps and automorphic forms*

Kollár/Mori, *Birational geometry of algebraic varieties*

~~Lang, ~~*Algebra*

Lazarsfeld, *Positivity in algebraic geometry, I and II*

Milne, *Etale cohomology*

Mumford/Fogarty, *Geometric invariant theory*

Mukai, *An introduction to invariants and moduli*

Schwartz, *Unstable modules over the Steenrod algebra and Sullivan’s fixed point set conjecture*

Serre, *Cohomologie galoisienne*

Serre, *Linear representations of finite groups*

Seshadri, *Fibrés vectoriels sur les courbes algebriques*

Voisin, *Hodge theory and complex algebraic geometry, I and II*

Dear Burt,

This is my favourite kind of post. By the way, may I ask what “finishing my book” refers to?

Artie,

I’m glad you like these — they’re easy to write.

I’m writing a short book called

Group cohomology and algebraic cycles. I wrote one paper about this in the 90s and always thought I should say more. Recent impetus has come from a paper by Peter Symonds in which he proved the first good bound on the cohomology of finite groups; see “On the Castelnuovo-Mumford Regularity of the Cohomology Ring of a Group,” available on his webpage http://www.maths.manchester.ac.uk/~pas/preprints/Wow… That’s a lot of books. I wonder how would it be if you didn’t travel light 😉

I did omit Lang’s

Algebraafter further careful pondering.I love real paper books/journals, much more than looking at them on the computer. But I usually take books going to various places ending up having too many things in my head to get to the books, keeping them in my hands without reading them until time is over, or I only manage to look at a few paragraphs in several hours.

Do you do a bit the same? Do you take those books expecting that in the end you will mostly not use them, just wanting to be sure you will not miss them if you do need them? Do you also prefer paper to looking at pdfs?

Also. Do you have preprints of your upcoming book?

And Schwartz’s book on unstable modules over the Steenrod algebra: I am curious why you have/take it? What concepts in it relate to your interests? If you felt like commenting about its contents, sharing any insight, I would be very interested.