Algebraic Atiyah-Singer index theorem

Abstract

The aim of this work is to give an algebraic weak version of the Atiyah-Singer index theorem. We compute then a few small examples with the elliptic differential operator of order $\le 1$ coming from the Atiyah class in ${\mathrm{Ext}}_{{\mathcal{O}}_X}^1({\mathcal{O}}_X,{\Omega }_{X/k}^1)$, where $X⟶\mathrm{Spec}(k)$ is a smooth projective scheme over a perfect field $k$.

arXiv commenttypos fixed, some small examples are added