Serre's modularity conjecture: The level one case

By Chandrashekhar B. Khare. 2006

90 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ea7e9567d287e9e7802b155ba7b730cb12c7416

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. M. Kisin
2. J.-P. Wintenberger
3. Jean-Pierre Wintenberger
4. Barry Mazur
5. Chandrashekhar B. Khare

In Geometry and Topology

1. Jean-Pierre Wintenberger
2. Barry Mazur
3. Chandrashekhar B. Khare
4. J.-P. Wintenberger
5. M. Kisin
6. T. Gee
7. Frank Calegari
8. David Geraghty

In Mathematical Physics

1. Jean-Pierre Wintenberger
2. Barry Mazur
3. Chandrashekhar B. Khare
4. J.-P. Wintenberger
5. M. Kisin
6. T. Gee
7. Frank Calegari
8. David Geraghty

Citations in the corpus

• Modularity of 2-adic Barsotti-Tate representations (2009, result): “This result was proved by Khare [ 11 ]f or¯ ρ of conductor 1, and by Khare-Wintenberger [13 ]f or¯ ρ of odd conductor.”
• On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q) (2009, methodology): “Note that we are allowing p = 3 as it is explained in [27] how to extend the results of [50] to this case.”
• Finding meaning in error terms (2008, background): “Multiple such hops (an inductive argument being in play) were at work in Khare’s orginal work [21] on Serre’s Conjecture for level 1, and also in the full proof of Serre’s Conjecture by Khare and Wintenberger.”
• Serre’s modularity conjecture (II) (2009, methodology): “The following theorem had been conjectured by Serre ([32]) and is proved in ([20], [18], [21], [22]):”