2024 Deformations of galois representations

Deformations of galois representations

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August undefined, 2024

WebDeformation of Galois Representations Chung Pang Mok 1. Introduction As before, let p be an odd prime, N an integer prime to p. Let S be the set of primes dividing N, together with p and ∞. Recall that GQ,S is the Galois group of the maximal extension of Q unramiﬁed outside S. Consider a representation: ρ¯: GQ,S → GL2(Fp)

Demuškin Groups with Group Actions and Applications to Deformations …

WebGalois representations, removing or relaxing many of the hypotheses of part I. We are able to prescribe local conditions on our deformations by allowing ramification at a set of primes congruent to 1 mod p, not 1 mod p2, and satisfying some other splitting conditions. The new hypotheses admit WebThe central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ... crickweb ks2 literacy

Deformation of rigid conjugate self-dual Galois representations

WebWe determine the universal deformation ring, in the sense of Mazur, of a residual representation $\bar \rho :G_K\to {\rm GL}_2(k)$, where k is a finite field of characteristic p and K is a local field of residue characteristic p.As one might hope for, but is not proven in the global case, the deformation ring is a complete intersection, flat over W(k), with the … WebREVIEW OF GALOIS DEFORMATIONS 3 More generally, if δ: GL N →GL M is a homomorphism of group schemes, we get a natural map of deformation rings R(δ(ρ)) … WebFeb 7, 2008 · Request PDF On Feb 7, 2008, Fernando Q. Gouvêa published Deformations of Galois representations Find, read and cite all the research you … crick wooden lid

Arithmetic of p-adic Modular Forms SpringerLink

DEFORMATIONS OF GALOIS REPRESENTATIONS - Stanford …

http://virtualmath1.stanford.edu/~conrad/modseminar/pdf/L19.pdf WebDEFORMATIONS OF GALOIS REPRESENTATIONS ANDREEA IORGA Abstract. These are notes for a talk on Galois deformations, focusing on Euler characteristic formulas … budget esper artifacts edhWebgeometric Galois representation. In this paper, we study the nearly ordinary deformations of ρ. When Kis totally real and ρis modular, results of Hida imply that the nearly ordinary deformation space associated to ρ contains a Zariski dense set of points corresponding to“automorphic” Galois representations. We conjecture crickwing read aloud

"Webp-ADIC HODGE THEORY AND DEFORMATIONS OF GALOIS REPRESENTATIONS 5 1.4. Local elds in mixed characteristic. Let K=Q p be a nite extension, and let G K = Gal(K=K). Then we ask the same questions as before: we want to describe continuous representations of G K on nitely generated (1) F p-vector spaces, (2) Z p-modules, or … " - Deformations of galois representations

Deformations of galois representations

WebTwo-dimensional p-adic Galois representations unramified away from p, Compositio Math 74 (1990), 115–133. MathSciNet MATH Google Scholar An “infinite fern” in the … WebDeformations of Galois representations and exceptional monodromy (Inventiones Mathematicae 205 (2)) For any simple algebraic group G of exceptional type, this paper constructs geometric l-adic representations with algebraic monodromy group G. Along the way it establishes a generalization to any reductive group of Ravi Ramakrishna's lifting ...

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WebThen we prove the existence of deformations arising from cuspforms on GL 2 (A F) via the Galois representations constructed by Taylor et al. We establish a sufficient condition (in terms of the non-existence of certain field extensions which in many cases can be reduced to a condition on an L -value) for the universal deformation ring to be a ... Web3.2. Level raising deformations 9 3.3. Fontaine-Laﬀaille deformations 10 4. Cohomology of certain quaternionic unitary Shimura variety 12 4.1. Taylor-Wiles System 15 5. Rigidity …

WebGENERAL GALOIS DEFORMATIONS 4 v ˆcompletely determines ˆ v ˆ= 0 mod m R We say ˆis well-placed if v ˆlands in V R M n(R)r.The key is that Lemma 3.6. If ˆ: G!GL n(R) is a … WebMar 17, 2024 · We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring R classifying deformations of a fixed Galois representation to simplicial …

WebDEFORMATIONS OF GALOIS REPRESENTATIONS MISJA STEINMETZ A talk in the Derived Structures in the Langlands Program study group at UCL in Spring 2024. These are notes taken by Ashwin Iyengar ([email protected]), edited by Misja Steinmetz. 1. Introduction Why would one be interested in studying the deformation theory of Galois … WebREVIEW OF GALOIS DEFORMATIONS 3 More generally, if δ: GL N →GL M is a homomorphism of group schemes, we get a natural map of deformation rings R(δ(ρ)) →R(ρ). Deformation rings also commute with tensor products of representations. Let π,ρ be two absolutely irreducible residual representations whose tensor product is also …

WebAug 16, 2024 · Abstract. In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois ...

WebAug 1, 2016 · Download Citation Deformations of Galois representations and exceptional monodromy For any simple algebraic group G of exceptional type, we … budget estimate and revised estimate pptWebbackground on Galois cohomology of number fields, deformations of Galois representations, p-adic Hodge theory, modular forms for GL_2(Q), the Langlands correspondence and commutative algebra will be surveyed along the way. Warning for the experts: there have been a lot of new ideas introduced budget essay in englishWebSep 1, 2024 · Chapters 4 and 5 give a deep insight into the deformation theory of Galois representations: we construct the deformation functors Dρ and D ,ψ ρ and the universal deformation ring R univ ρ ... crickwire activation not workingWebAug 25, 2016 · We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring $\\mathcal{R}$ classifying deformations of a fixed Galois representation to simplicial coefficient rings; its zeroth homotopy group $π_0 \\mathcal{R}$ recovers Mazur's deformation ring. We give evidence that these rings $\\mathcal{R}$ occur in the wild: For … crick wooderWebAug 5, 2016 · This paper enhances the deformation-theoretic techniques of [] and strengthens the applications in that paper to the construction of geometric Galois representations with exceptional algebraic monodromy groups.The foundation of the deformation-theoretic method of [] is an ingenious idea of Ramakrishna ([13, 14]), which … budget estimate and financial analysis翻译WebDocumenta Math. 573 On the Structure of Selmer Groups of Λ-AdicDeformations over p-AdicLie Extensions SudhanshuShekharand R. Sujatha Received: September 14,2011 … crick wooder bandhttp://virtualmath1.stanford.edu/~conrad/modseminar/pdf/L19.pdf crickwood