I have found many interesting statements in the language of algebraic geometry etc. but by lack of literacy I am not able to destill out what concretely a "derived modular form" or "deriver graded character" of a VOA should be, in any simple example. "Factorization algebra" and "Gwilliam" was a very good suggestion, thanks! Particular for my question seems to be "Factorization algebras in quantum field theory" by Costello and Gwilliam. I cant digest this right away, but I saw smth about n-forms and also about higher coefficients in an hbar-expansion....

Ah, hallo :-) I guess I ask both,

Carlo, that would be great - do you have a reference? I would somehow expect that, but the proofs I found where too involved for myself to easily include additional potential terms (e.g. the binomial formula for V(x+deltax) does not hold if I include a cut-off)?

That was fast and exactly what I wanted to know. I appreachiate it a lot, thank you!

Yes, with "sphere" I meant those varieties. @skd: I agree that onncommutativity of $SO_3\mathbb({F}_q)$ shows but my question is: I want additional structure on the variety (metric, connection or simliar thing) that produce a CHOICE of say an $SO_3\mathbb({F}_q)$-element for each pair of point $x\mapsto y$.