On Faltings' main comparison theorem in p-adic Hodge theory: the relative case
Student No.:80
Time:Fri 16:30-17:30, Nov.9
Instructor:Ahmed Abbes  
Place:Lecture hall, Jin Chun Yuan West Bldg.
Starting Date:2018-11-9
Ending Date:2018-11-9

The raison d'être of p-adic Hodge theory are the comparison theorems between p-adic étale cohomology of a smooth proper variety over a p-adic field and other p-adic cohomologies of differential nature (Hodge, de Rham, crystalline...). Faltings' approach for this theory is up to now the most successful. He obtained all comparison theorems from a basic one, namely his main comparison theorem. In the first part of my lecture, I will explain this theorem and in the second part, I will discuss a relative version roughly sketched by Faltings in the appendix of his 2002 Astérisque article. The actual proof requires more work (joint with Michel Gros): as one says, the devil is in the details...

About speaker:
Ahmed Abbes is director of research at the French National Center for Scientific Research (CNRS) and the Institute of Advanced Scientific Studies (IHÉS) in Paris. He mainly studies geometrical and cohomological properties of sheaves on varieties on perfect fields of characteristic p>0 or on p-adic fields, designed for applications in arithmetic and algebraic geometry.
His joint work with Takeshi Saito (Tokyo) led to a significant breakthrough in ramification theory. His recent work focuses on p-adic Hodge theory. He developed jointly with Michel Gros the p-adic Simpson correspondence initiated by G. Faltings.

p进位霍奇理论存在的原因是p进位域上的光滑恰当簇的p进位étale上同调和其他不同性质(霍奇、德拉姆、晶体)的p进位上同调之间的比较定理。法尔廷斯的方法是到目前为止最成功的,他通过最基本的,即他的主要比较定理得到了所有比较定理。在本讲的第一部分,报告人将阐释该定理;在第二部分,报告人将讨论一个在其2002年的Astérisque的附录中法尔廷斯给出简略思路的相关版本。真正的证明需要下更多功夫(与Michel Gros合作):如人所云,恶魔在细节中……

Ahmed Abbess教授,法国国家科学研究中心和巴黎高级科学研究所研究部主任,主要研究特征数p>0或p进位的完美域簇上层的几何及上同调性质,用于算术和代数几何。
Abbess教授与Takeshi Saito(东京)就分歧理论方面的合作取得重大突破。最近他的工作重点是p进位霍奇理论,并与Michel Gros共同研究了基于法尔廷斯方法的p进位辛普森对应。