The Fontaine-Mazur conjecture for {GL}_2

By M. Kisin. 2009

234 citations recorded by the source corpus.

Introduction 641 1. Breuil-Mezard conjecture and the p-adic local Langlands 644 (1.1) The Breuil-Mezard conjecture 644 (1.2) Review of Colmez’s functor 647 (1.3) Hilbert-Samuel multiplicities 650 (1.4) Representations and pseudo-representations 653 (1.5) GL2(Qp)-representations mod p. 657 (1.6) Local patching and multiplicities 661 (1.7) From pseudo-representations to representations 669 2. Modularity via the Breuil-Mezard conjecture 675 (2.1) Quaternionic forms 675 (2.2) Global patching and multiplicities 677 (2.3) The Breuil-Mezard conjecture 686 Addendum to [Ki 1] 687 References 689

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/18fe1cddca1f79fc1bb0b66fd3b410dfa69e0ad3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. T. Gee
2. Peter Scholze
3. Kiran S. Kedlaya
4. Tongyin Liu
5. Ruochuan Liu
6. C. Breuil
7. M. Kisin
8. Barry Mazur

In Mathematical Physics

1. T. Gee
2. Peter Scholze
3. Kiran S. Kedlaya
4. Ruochuan Liu
5. Tongyin Liu
6. C. Breuil
7. M. Kisin
8. Barry Mazur

Citations in the corpus

• Automorphic lifts of prescribed types (2008, methodology): “To our knowledge, the only such theorems in the literature are those for weight two Hilbert modular forms in [13,24], and the work of [ 26 ]f or modular forms over totally real fields in which p splits completely.”
• The emerging p-adic Langlands programme (2011, background): “For instance it allowed Kisin to give in many cases another construction of B(V ) more amenable to deformation theory ([46]) and it was a key ingredient in Kisin’s or Emerton’s proof of almost all cases of the Fontaine-Mazur conjecture ([45], [28]).”
• Finding meaning in error terms (2008, background): “(26)See [26] where the [LC(v)] condition for v|p > 2 is that the local representation is Barsotti-Tate; [27] deals with p = 2; and [28] covers the case where the local representations for v|p become semi-stable over an abelian extension of Qp; consult Kisin’s web-page for more: http://www.”
• Relative P-adic Hodge Theory: Foundations (2013, background): “(see for instance [23]) and has led to important advances concerning modularity of Galois representations, in the direction of the Fontaine-Mazur conjecture [76], [36].”
• Torsion p-adic Galois representations and a conjecture of Fontaine (2007, background): “For the same condition P, (3) is established in [16], which is sufficient for applications to modularity theorems as in [15] (whereas (1) is not).”
• Serre’s modularity conjecture (II) (2009, unknown): “Kisin ([24]):”