Algebraic Atiyah-Singer index theorem

2017/02/08 by Nguyen Le Dang Thi, Thi, Nguyen Le Dang
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1702.02625

openalex publication_date 2017/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ≤ 1 coming from the Atiyah class in Ext¹_OX(O_X,Ω¹_X/k), where X \longrightarrow Spec(k) is a smooth projective scheme over a perfect field k.

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