Deformation rings and parabolic induction
نویسندگان
چکیده
منابع مشابه
Eisenstein deformation rings
We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring ...
متن کاملSome Computations with Heeke Rings and Deformation Rings
In order to prove that semistable elliptic curves E over Q are modular, A. Wiles [Wiles 95] considers the Galois representation ρ : Gal(Q/Q) −→ GL2(F3) provided by the 3-torsion points E[3] of a semistable elliptic curve E. He proves that certain rather restricted deformations of ρ are modular. It follows then that, in particular, the deformation provided by the Galois representation ρE : Gal(Q...
متن کاملPresentations of universal deformation rings
Let F be a finite field of characteristic ` > 0, F a number field, GF the absolute Galois group of F and let ρ̄ : GF → GLN (F) be an absolutely irreducible continuous representation. Suppose S is a finite set of places containing all places above ` and above ∞ and all those at which ρ̄ ramifies. Let O be a complete discrete valuation ring of characteristic zero with residue field F. In such a sit...
متن کاملPotentially Semi-stable Deformation Rings
LetK/Qp be a finite extension and GK = Gal(K̄/K) the Galois group of an algebraic closure K̄. Let F be a finite field of characteristic p, and VF a finite dimensional F-vector space equipped with a continuous action of GK . The study of the deformation theory of Galois representations was initiated by Mazur [Ma], who showed that if VF has no non-trivial endomorphisms, then it admits a universal d...
متن کاملSingularities of Ordinary Deformation Rings
Let R be the universal deformation ring of a residual representation of a local Galois group. Kisin showed that many loci in MaxSpec(R[1/p]) of interest are Zariski closed, and gave a way to study the generic fiber of the corresponding quotient of R. However, his method gives little information about the quotient ring before inverting p. We give a method for studying this quotient in certain ca...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2018
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.1046