By this time I’m sure everyone whose curiousity was piqued by the statement of the Grothendieck-Riemann-Roch theorem has read it themselves. Nevertheless, in case you haven’t, I will proceed to outline the steps of the surprisingly “easy” proof. It is “easy” in the sense that the most is made of a relatively simple computation on projecive space. Last time we saw that it is enough to prove the formula separately for an injection and a projection. We’ll see here how to carry these two steps through and how the first may be reduced to the inclusion of a divisor. Though last time I said that I wanted to go into each step in more detail, I realized that 1) probably very few people are (still?) following along, 2) for those who are, they will get more by seeing an outline and reading the paper or looking at Fulton’s Intersection Theory themselves, and 3) this way we can illustrate the power of the theorem with some applications.

### June 2009

June 9, 2009

## The Grothendieck-Riemann-Roch Theorem, a proof-sketch

Posted by Matt DeLand under Algebraic Geometry, Big Theorems, Cohomology[4] Comments

June 8, 2009

As I mentioned, I’m participating in a summer school on the Geometry of Quantum Fields at Penn. I’m in Katrin Wendland’s mentoring session this week, which means conformal fields and vertex algebras.

June 3, 2009

I know I’ve been fairly bad about posting recently. Started teaching my first course. But that SHOULD end on Monday. Not the course, the silence. That’s when the Geometry of Quantum Fields summer school starts here at Penn. For the first week, I’m going to be attempting to learn what a Conformal Field is with Katrin Wendland, and I’ll be attempting to blog about it. The next week, I’m with Eric Sharpe, talking about Heterotic Compactifications and Quantum Cohomology. The posts these next two weeks will be rather technical, but afterwards, I’ll probably attempt to distill them and provide some background and motivation beyond whatever else is covered. Might also blog on some of the talks, but those are the two mentoring sessions I’m in, so they’ll be the most in-depth.