“
—— David Hilbert
I have been interested in
Algebraic Number Theory and Arithmetic Geometry since 1995, when I was a
graduate student in
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:
[16] Compatibility of Kisin modules for different uniformizers, preprint, (pdf)
[15] A Note on Potential Diagonalizability of Crystalline Representations, (with Hui Gao), preprint, (pdf)
[14] The Buzzard-Diamond-Jarvis conjecture for unitary groups , (with Toby Gee and David Savitt), preprint, (arXiv)
[13] Crystalline extensions and the weight part of Serre's conjecture, (with Toby Gee and David Savitt), Algebra & Number Theory, Vol. 6 (2012), No. 7, 1537-1559 (arXiv)
[12] Filtration associated to torsion semi-stable representations, preprint (pdf)
[11] The correspondence between Barsotti-Tate groups and Kisin modules when p=2 , preprint (pdf)
[10] Galois Representations with Quaternion Multiplications Associated to Noncongruence Modular Forms , (with A.O.L. Atkin, Wen-Ching Winnie Li, Ling Long), preprint, appear at Transactions of of AMS (arXiv)
[9] Lattices in filtered (φ, N)-modules, J. Inst. Math. Jussieu 2, Volume 11, Issue 03, 2012, pp 659-693 (pdf) ((Errata in the end of [16]) )
[8] Some Bounds for ramification of p^n-torsion semi-stable representations , (with Xavier Caruso), Journal of Algebra, 325, 2011, Issue 1, 70-96 (arXiv)
[7] A note on lattices in semi-stable representations, Mathematische Annalen, 346, (2010), No. 1, 117--138. (PDF)
[6] Quasi-semi-stable representations, (with Xavier Caruso), Bull. Soc. math. de France, 137 (2), 2009, p. 185-223 (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])
[4] On lattices in semi-stable representations: a proof of a conjecture of Breuil , Compositio Mathematica, 144, 2008, No. 1, 61--88, (PDF)
[3] Potentially Good Reduction of Barsotti-Tate Groups. Jounal of number theory, 126 (2007), no. 2, 155-184. (PDF)
[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) [1] Congruences for the class numbers of real cyclic sextic number fields. Sci. China Ser. A 42 (1999), no. 10, 1009--1018.
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