Yeah, I read the Lurie up to the IV I think, so VII will be welcome.

I'm sorry for the misunderstanding. What I meant was that you define det to be some number if your scheme if the scheme gives a finite answer, so, no, I don't know any scheme to make det(2*I) finite.

Ok, it's certainly my mistake --- I basically thought det exp A is defined as exp tr A which would make (1) trivial. But for the reference, I think books.google.com/… might help.

3-folds shouldn't be smooth, you can compute tangent space I think.

Wait, wait, ok. What's so good in the definition of the tmf that makes it so similar to integral modular forms?

The question is mathoverflow.net/questions/308/elliptic-curve-over-spectra

Wow, that's amazing. I don't know what would be the right way to proceed. It's probably easiest if I make a separate question about analogues of elliptic curves over spectra, sorry to ask so much!

It really would be an injustice to mark just one answer as the accepted one...

Yeah, Golden ratio been here from ancient times.

Indeed, I forgot about the rep restriction. Actually, once there are many people here, you'll be getting a high rep very fast. Here's +10 for you :) but please remove the (3) as the answer is known to be positive by 3 other answers.

Also, what's the problem with links? Is it because they need to be escaped like in tip 7 of mathoverflow.net/tips?