Galois representations
Explicit computations with modular Galois representations
... On the other hand, research on the computational aspects of modular Galois representations is still in its early childhood. At the moment of writing this thesis there is very little literature on this ...
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Oddness of residually reducible Galois representations
... dual) Galois representations of CM fields to prove part of the Bloch–Kato conjecture for general Asai (or tensor induction) L-functions, our main result in Theorem ...polarized Galois representation ...
17
Special Frobenius Traces in Galois Representations
... is irreducible unless ρ is of cyclic or dihedral type. In Proposition 2.3.2 we prove that for n = 3, Ad(ρ) is irreducible in precisely four cases; two of which yield simple groups and the remaining two yield solvable ...
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Images of adelic Galois representations for modular forms
... of Galois representations; this is to exhibit cer- tain special elements in the images of the tensor product Galois representations ρ f,p ⊗ ρ g,p whose existence is important in Euler system ...
15
Black box Galois representations
... Box Galois representations come from Bianchi modular newforms with rational Hecke ...suitable Galois representations in this case was first devel- oped by Taylor et ...
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Computational aspects of Galois representations
... integral Galois representations; this is due to the fact that for two different integral Galois representations coming from two different stable lattices, we may not have that they are ...
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On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields
... In this section we will state our main theorems (Theorems 8.1, 8.2 and 8.5) for the two-dimensional Galois representations over imaginary quadratic fields considered in section 7. In this case many of the ...
30
Certification of modular Galois representations
... about Galois representations attached to mod- ular forms and how we used these in [Mas13] to compute Fourier coefficients of modular forms in section ...
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Images of Galois representations
... modular Galois representations, under the supervision of Professor Luis Dieulefait at the Universitat de Barcelona and Professor Alberto Canonaco at the Uni- versità degli Studi di Pavia, and he received ...
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Four dimensional Galois representations of solvable type and automorphic forms
... Many people have helped shape this thesis, some more directly than others. I would especially like to thank the following: Michael Aschbacher, for always being able to tell me anything I wanted to know about finite ...
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Rankin Eisenstein classes in Coleman families
... 7. Bosch, S., Güntzer, U., Remmert, R.: Non-Archimedean analysis. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 261, Springer, Berlin (1984). ...
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Companion forms and explicit computation of PGL2 number fields with very little ramification
... compute Galois representations attached to forms admitting a companion mod ℓ, and for pro- viding the author with a few examples of such forms that were especially amenable to computation, and Ariel Pacetti ...
32
Euler systems for Rankin Selberg convolutions of modular forms
... p-adic Galois representations of pairs of weight 2 modular forms, and related their image under the Bloch–Kato logarithm maps to the values of p-adic Rankin–Selberg ...
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The Proof of the Fermat’s Conjecture in the Correct Domain
... In the article by Andrew J. Wiles, there is no conclusive formula where any substitution with concrete natural numbers a, b, c, n would confirm the Fermat’s Conjecture. Except mentioning the Fermat’s Last Theorem by name ...
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... current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various ...of Galois groups of p-extensions is an important step toward a ...counting ...
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On the Galois structure of Selmer groups
... Abstract. Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the ...
17
Discrete Logarithm in Galois Rings
... use Galois rings to perform ElGamal encryption through the concept of the discrete logarithm and the ...in Galois rings GR(p k , m) allows to express each element α ∈ GR(p k , m) in the form: α = ξ (x 0 ,x ...
12
On characterizations of a center Galois extension
... center Galois extension of B G (that is, C is a Galois algebra over C G with Galois group G| C G) if and only if the ideal of B generated by{c − g(c) | c ∈ C} is B for each g ≠ 1 in ...commutative ...
6
On separable group rings
... Moreover, Galois extensions of a ring satisfying the fundamental theorem were studied in ...the Galois map for a non-Galois extension RG of (RG) G ...
8
Cohomology of Absolute Galois Groups
... The proof of this theorem one commonly refers to nowadays is due to L. Ribes (1977, see also [RZ10, § 2.11]). Note that the aforemen- tioned theorem does not say anything about the nature of the field K nor about the ...
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