This joint seminar aims to understand the paper p-adic deformation of algebraic cycle classes[pdf] by Spencer Bloch, Hélène Ensault and Moritz Kerz, in which they studied the p-adic deformation properties of algebraic cycle classes modulo rational equivalence, and showed that the crystalline Chern character of a vector bundle lies in a certain part of the Hodge filtration if and only if, rationally, the class of the vector bundle lifts to a formal pro-class in K-theory on the p-adic scheme.
- Joint Seminar Plan [pdf]
- Talk 1: Variation of Hodge Conjecture by Sheng Mao [pdf]
- Talk 2: Homological and homotopical algebra by Zheng Weizhe [pdf]
- Talk 3: A reminder on crystalline cohomology by Wang Shanwen
- Talk 4: Chern classes in crystalline cohomology by Tong Jilong [pdf]
- Talk 5: Line Bundle Case by Pan Xuanyu [pdf]
- Talk 6: Crystalline and dR cohomology by Sheng Mao [pdf]
- Talk 7: Syntompic complex by Zhang Lei [pdf]
- Talk 8: Fundamental Triangle by Wu Han [pdf]
- Talk 9: Nisnevich topology by Xu Jinxing [pdf]
- Talk 10: Motivic cohomology by Sheng Mao [pdf]
- Talk 11: Motivic Pro-complex by Li Muxi [pdf]
- Talk 12: Crystalline-Hodge obstruction by Tong Jilong [pdf]
- Talk 13: Beilinson's motivic pro-complex by Shentu Junchao [pdf]