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arXiv · 1702.02625

Algebraic Atiyah-Singer index theorem

Nguyen Le Dang Thi
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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 $\leq 1$ coming from the Atiyah class in $\mathrm{Ext}^1_{\mathcal{O}_X}(\mathcal{O}_X,\Omega^1_{X/k})$, where $X \longrightarrow \mathrm{Spec}(k)$ is a smooth projective scheme over a perfect field $k$.

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Nguyen Le Dang Thi. 2017-02-08. Algebraic Atiyah-Singer index theorem. https://arxiv.org/abs/1702.02625

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