Moduli of finite flat group schemes, and modularity

@inproceedings{Kisin2009ModuliOF,
  title={Moduli of finite flat group schemes, and modularity},
  author={Mark Kisin},
  year={2009}
}
We prove that, under some mild conditions, a two dimensional p-adic Galois representation which is residually modular and potentially Barsotti-Tate at p is modular. This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture, especially for elliptic curves which acquire good reduction over a wildly ramified extension of ℚ 3 . The main ingredient is a new technique for analyzing flat deformation rings. It involves resolving them by spaces which parametrize finite… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 99 CITATIONS

Kisin-Ren classification of w¯-divisible O-modules via the Dieudonne Crystal

VIEW 34 EXCERPTS
CITES METHODS
HIGHLY INFLUENCED

G-valued crystalline representations with minuscule p-adic Hodge type

VIEW 13 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Estimation des dimensions de certaines vari\'et\'es de Kisin

VIEW 20 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Computation of Framed Deformation Functors

VIEW 7 EXCERPTS
CITES RESULTS, BACKGROUND & METHODS
HIGHLY INFLUENCED

Geometric level raising and lowering on the eigencurve

VIEW 15 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Breuil-Kisin modules and Hopf orders in cyclic group rings

VIEW 4 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Failure of the Local to Global Principle in the Eigencurve

VIEW 15 EXCERPTS
CITES BACKGROUND, METHODS & RESULTS
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

2007
2020

CITATION STATISTICS

  • 15 Highly Influenced Citations

References

Publications referenced by this paper.
SHOWING 1-10 OF 39 REFERENCES

MANOHARMAYUM, On the modularity of supersingular elliptic curves over certain totally real number fields

  • J. F. JARVIS
  • J. Number Theory
  • 2008

SAVITT, On a conjecture of Conrad, Diamond, and Taylor

  • D. Sav
  • Duke Math. J
  • 2005

MÉZARD, Multiplicités modulaires et représentations de GL2.Zp/ et de Gal.Qp=Qp/ en l D

  • A. C. BREUIL
  • p, Duke Math. J
  • 2002

KHARE, A local analysis of congruences in the .p

  • C. Kh
  • p/ case. II, Invent. Math
  • 2001

WILES, Base change and a problem of Serre

  • A.J.C.M. SKINNER
  • Duke Math. J
  • 2001