Invariants of projective space III: Motives

Monday, December 10th, 2012 | Author:

I want to explain a particularly easy example of a motivic cellular decomposition: That of n-dimensional projective space. The discussion started with cohomology (part 1), continued with bundles and cycles (part 2) and in this part 3, we discuss motivic stuff.

Continue reading «Invariants of projective space III: Motives»

Category: English, Mathematics | Comments off

Invariants of projective space II: Cycles and Bundles

Thursday, December 06th, 2012 | Author:

I want to explain a particularly easy example of a motivic cellular decomposition: That of n-dimensional projective space. The discussion started with cohomology (part 1) and in this part 2, we discuss intersection-theoretic and bundle-theoretic invariants. In part 3 we will see the motivic stuff.

Continue reading «Invariants of projective space II: Cycles and Bundles»

Category: English, Mathematics | Comments off

Invariants of projective space I: Cohomology

Tuesday, December 04th, 2012 | Author:

I want to explain a particularly easy example of a motivic cellular decomposition: That of n-dimensional projective space. We will have a look at the cohomology, the Chow groups and the algebraic K-theory of projective space -- a discussion probably interesting to non-motivic people as well. After these invariants, I will look at the motive and the A¹-homotopy type. Then I want to describe the decomposition of the motive (and the homotopy type) homotopy-theoretically, by means of cofiber sequences. (We will see that projective space is not isomorphic to a coproduct of motivic spheres with the same motive). Of course, nothing is new, I'm just working out exercises here.

In this part 1, I discuss only the cohomology of \mathbb{P}^n. Part 2 contains a discussion of the intersection theory and bundles and part 3 contains the motivic stuff. I intentionally left out usage of projective bundle formulas, as I will discuss them separately.

Continue reading «Invariants of projective space I: Cohomology»

Category: English, Mathematics | Comments off