“Wir müssen wissen, Wir werden wissen”

                                     —— David Hilbert

I have been interested in Algebraic Number Theory and Arithmetic Geometry since 1995, when I was a graduate student in Tsinghua University, China.  Right now I have been focusing on  p-adic Galois representations from algebraic geometry, more specifically, integral p-adic Hodge theory.  

 

Roughly speaking, integral p-adic Hodge theory is the study of Galois stable Z_p lattices in semi-stable p-adic representations together with their links with the various integral p-adic cohomologies of proper smooth scheme over base fields F. It gives rise to p-torsion phenomena which makes the theory very complicated. For the introduction of integral p-adic Hodge theory, please see Breuil's survey paper " Integral p-adic Hodge Theory".     

 

 

 

Preprints and Publications: 

[1] Congruences for the class numbers of real cyclic sextic number fields.    Sci. China Ser. A 42 (1999), no. 10, 1009--1018.

[2] Steinitz class of Mordell-Weil groups of elliptic curves with complex  multiplication.  (with Xiake Zhang), Pacific J. Math.193 (2000), no. 2, 371--379.(DVI)

[3] Potentially Good Reduction of Barsotti-Tate Groups. Jounal of number theory, 126 (2007), no. 2, 155-184. (PDF)  

[4] On lattices in semi-stable representations: a proof of a conjecture of Breuil , Compositio Mathematica, 144, 2008, No. 1, 61--88, (PDF)

[5] Torsion p-adic Galois representation and a conjecture of Fontaine, Ann. Scient. de l'E.N.S., Volume 40, Issue 4, July-August 2007, Pages 633-674. (PDF) (Errata in the end of [7])

[6] Quasi-semi-stable representations, (with Xavier Caruso), Bull. Soc. math. de France, 137 (2), 2009, p. 185-223 (PDF)

[7] A note on lattices in semi-stable representations, preprint, appear at Mathematische Annalen (PDF)

[8] Some Bounds for ramification of p^n-torsion semi-stable representations , (with Xavier Caruso), preprint (arXiv)

[9] Lattices in filtered (j, N)-modules, preprint, (pdf)

 

Notes (Please be aware of typoes and mistakes, use very carefully):

 

[1] CM Seminar Notes,  Classification of Abelian Varieties with CM over C and Reduction of Abelian Varieties. (PDF) 
  The link to 2004-05 VIGRE Number Theory Working Group
[2] Mini course in Morningside center on an introduction to p-adic Hodge theory: Note1, Note2

 

[3] Modularity of compatible family of p-adic Galois representations PDF

 
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