تقرير
Intersection de Rham complexes in positive characteristic
| العنوان: | Intersection de Rham complexes in positive characteristic |
|---|---|
| المؤلفون: | Sheng, Mao, Zhang, Zebao |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14C30, 14D07, 14F43, 14G17 |
| الوصف: | We establish a positive characteristic analogue of intersection cohomology theory for variations of Hodge structure. It includes: a) the de Rham-Higgs comparison theorem for the intersection de Rham complex; b) the $E_1$-degeneration theorem for the intersection de Rham complex of a periodic de Rham bundle; c) the Kodaira-Saito vanishing theorem for the intersection cohomology groups of a periodic Higgs bundle. These results generalize the decomposition theorem of Deligne-Illusie and the de Rham-Higgs theorem of Ogus-Vologodsky, the $E_1$-degneration theorem of Deligne-Illusie, Illusie, Faltings and the Kodaira-Saito vanishing theorem of Arapura. As an application, we give an algebraic proof of the $E_1$-degeneration theorem due to Cattani-Kaplan-Schmid and Kashiwara-Kawai, and the vanishing theorem of Saito for VHSs of geometric origin. Comment: Third version. Replace the second version entitled 'On the decomposition theorem for intersection de Rham complexes'. 42 pages. Comments are greatly appreciated |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1904.06651 |
| رقم الأكسشن: | edsarx.1904.06651 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |