Nonabelian Hodge theory in positive characteristic via exponential twisting

作者：Lan Guitang^*; Sheng Mao; Zuo Kang

来源：Mathematical Research Letters, 2015, 22(3): 859-879.

DOI：10.4310/mrl.2015.v22.n3.a12

Let k be a perfect field of positive characteristic and X a smooth algebraic variety over k which is W-2-liftable. We show that the exponent twisiting of the classical Cartier descent gives an equivalence of categories between the category of nilpotent Higgs sheaves of exponent <= p over X/k and the category of nilpotent flat sheaves of exponent <= p over X/k, by showing that it is equivalent up to sign to the inverse Cartier and Cartier transforms for these nilpotent objects constructed in the nonabelian Hodge theory in positive characteristic by Ogus-Vologodsky [10]. In view of the crucial role that Deligne-Illusie's lemma has ever played in their algebraic proof of E-1-degeneration of the Hodge to de Rham spectral sequence and Kodaira vanishing theorem in abelian Hodge theory, it may not be overly surprising that again this lemma plays a significant role via the concept of Higgs-de Rham flow [8] in establishing a p-adic Simpson correspondence in the nonabelian Hodge theory and Langer's algebraic proof of Bogomolov inequality for semistable Higgs bundles and Miyaoka-Yau inequality [9].

• 出版日期2015
• 单位中国科学技术大学