Even Galois representations and the Fontaine–Mazur conjecture

By Frank Calegari. 2009

61 citations recorded by the source corpus.

We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})$ with distinct Hodge–Tate weights. This is in accordance with the Fontaine–Mazur conjecture. If K/Q is an imaginary quadratic field, we also prove (again, under certain hypotheses) that $\mathrm{Gal}(\overline{\mathbf{Q}}/K)$ does not admit irreducible two-dimensional ordinary Galois representations of non-parallel weight.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7b2fd52da053b2d1596f14d2caab9822373685e

How researchers see this paper

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In Algebra and Number Theory

1. Frank Calegari
2. Akshay Venkatesh
3. M. Emerton
4. T. Gee
5. M. Kisin
6. P. Michel
7. R. Munshi
8. V. Blomer

In Geometry and Topology

1. Akshay Venkatesh
2. M. Emerton
3. T. Gee
4. Frank Calegari
5. David Geraghty
6. J. Thorne
7. David Savitt
8. Vytautas Paškūnas

In Mathematical Physics

1. Akshay Venkatesh
2. M. Emerton
3. Frank Calegari
4. T. Gee
5. J. Thorne
6. David Geraghty
7. M. Kisin
8. David Savitt

Citations in the corpus

• A geometric perspective on the Breuil–Mézard conjecture (2011, background): “2 of [11]; in the notation of that result, we take G= Gn(F), and we let E be any totally real field with the property that, if v|p is a place of E, then Ev ∼= K.”
• A torsion Jacquet--Langlands correspondence (2012, background): “(Indeed, by work of the first author, one know nows in many cases that ρ admits no potentially semi-stable characteristic zero deformations [14, 15].”