Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur

By Ravi Ramakrishna. 2002

105 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/76cd940e79751b511322cdb207aebbe53b0de1f7

How researchers see this paper

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

In Algebra and Number Theory

1. Frank Calegari
2. J.-P. Wintenberger
3. Jean-Pierre Wintenberger
4. Barry Mazur
5. Chandrashekhar B. Khare
6. Akshay Venkatesh
7. Nicolas Bergeron

In Computational Mechanics

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

In Geometry and Topology

1. Frank Calegari
2. Jean-Pierre Wintenberger
3. Chandrashekhar B. Khare
4. J.-P. Wintenberger
5. Barry Mazur
6. Akshay Venkatesh
7. J. Thorne
8. T. Gee

Citations in the corpus

• The main conjecture of Iwasawa theory for totally real fields (2010, unknown): “Example Ramakrishna, in Corollary 1 of [32], constructs infinitely many surjective representation GQ → SL2(Z7) each of which is unramified outside a finite set of primes.”
• On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q) (2009, background): “Except in the case of k(ρ̄) = p+1 and R` is Rp,crys, this property of R` follows from the work of Ramakrishna ([34])”
• Serre’s modularity conjecture (II) (2009, background): “Ramakrishna was the first to construct geometric lifts under general hypotheses, but had to allow ramification at auxiliary primes ([27]).”
• Nearly ordinary Galois deformations over arbitrary number fields (2007, methodology): “146], we consider the restriction maps θ̃ and θ̃ (this notation defined exactly as in [33]).”