In this paper, we address the question of lifting vector bundles to Witt vector bundles. More precisely, let p be a prime number, and let S be a scheme of characteristic p. For any n greater than 2, denote by W_n(S) the scheme of Witt vectors of length n, built out of S. Question: is V the restriction to S of a vector bundle defined over W_n(S)? We give a positive answer to this question, provided S possesses an ample line bundle, with Theorem 3.7. Our strategy consists in first dealing with the particular case of tautological vector bundles over Grassmannian varieties over F_p. We finish by Corollary 3.9. Roughly speaking, it ensures the existence of an extension of V, to any prescribed lift S of S of characteristic p^n- up to Frobenius pullback. 查看全文>>