A conjecture of Morel asserts that the sheaf of –connected components of a space is –invariant. Using purely algebrogeometric methods, we determine the sheaf of –connected components of a smooth projective surface, which is birationally ruled over a curve of genus . As a consequence, we show that Morel’s conjecture holds for all smooth projective surfaces over an algebraically closed field of characteristic .
Chetan Balwe. Anand Sawant. "–connected components of ruled surfaces." Geom. Topol. 26 (1) 321 - 376, 2022. https://doi.org/10.2140/gt.2022.26.321