The Atiyah-Weil criterion for holomorphic connections (Q934318)

This article consists of a survey of the tools needed to prove the Atiyah-Weil criterion for a holomorphic vector bundle on a compact Riemann surface to admit a holomorphic connection and of \textit{M. F. Atiyah}'s proof [Trans. Am. Math. Soc. 85, 181--207 (1957; Zbl 0078.16002)] of this. There is also a generalization of this result to vector bundles over smooth projective curves when the base field is perfect and of any characteristic.