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See detailOn the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image
Deo, Shaunak UL

in Transactions of the American Mathematical Society (2018), 370(6), 3885-3912

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See detailDihedral Universal Deformations
Deo, Shaunak UL; Wiese, Gabor UL

E-print/Working paper (2018)

This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1 ... [more ▼]

This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic number theory, (3) modularity. As to (1), we prove that the universal deformation is dihedral if all infinitesimal deformations are dihedral. Concerning (2) in the setting of Galois representations of number fields, we give sufficient conditions to ensure that the universal deformation relatively unramified outside a finite set of primes is dihedral, and discuss in how far these conditions are necessary. As a side-result, we obtain cases of the unramified Fontaine-Mazur conjecture. As to (3), we prove a modularity theorem of the form `R=T' for parallel weight one Hilbert modular forms for cases when the minimal universal deformation is dihedral. [less ▲]

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See detailStructure of Hecke algebras of modular forms modulo $p$
Deo, Shaunak UL

in Algebra & Number Theory (2017), 11(1), 1-38

Detailed reference viewed: 87 (4 UL)