On lifting singular curves
From the introduction: A smooth projective curve over a field \(k\) lifts to any complete discrete valuation ring with residue field \(k\). This result extends to singular curves which are local complete intersections; one verifies that the corresponding obstruction in the cotangent complex vanishes (see [\textit{L. Illusie}, in: Fundamental algebraic geometry: Grothendieck's FGA explained. Mathematical Surveys and Monographs 123. Providence, RI: American Mathematical Society (AMS). (2005; Zbl 1085.14001), Cor. 8.5.32]). In this note we construct liftings of certain singular curves which are in general not local complete intersections. Our method is a straightforrward application of the result by \textit{C. Contou-Carrere} and \textit{D. Ferrand} [in: The Grothendieck Festschrift, Collect. Artic. in Honor of the 60th Birthday of A. Grothendieck. Vol. II, Prog. Math. 87, 69--109 (1990; Zbl 0752.14023), Bull. Soc. Math. Fr. 131, No. 4, 553--585 (2003; Zbl 1058.14003)] which extends the method of \textit{J. P. Serre} to construct pushouts of schemes.
scientific article; zbMATH DE number 6150653