Joshi, Kirti; Rajan, C. S. Frobenius splitting and ordinarity. (English) Zbl 1074.14019 Int. Math. Res. Not. 2003, No. 2, 109-121 (2003). Summary: We examine the relationship between the notion of Frobenius splitting and ordinarity for varieties. We show that the de Rham-Witt cohomology groups \(H^{i} (X,W({\mathcal O}_{X}))\) of a smooth projective Frobenius split variety are finitely generated over \(W(k)\). We provide counterexamples to a conjecture of Mehta that Frobenius split varieties are ordinary or even Hodge-Witt. Cited in 2 ReviewsCited in 16 Documents MSC: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14G27 Other nonalgebraically closed ground fields in algebraic geometry 14K05 Algebraic theory of abelian varieties PDFBibTeX XMLCite \textit{K. Joshi} and \textit{C. S. Rajan}, Int. Math. Res. Not. 2003, No. 2, 109--121 (2003; Zbl 1074.14019) Full Text: DOI