-extensions of  and arithmetic cohomology modulo 2.

Ash, Avner; Pollack, David; Soares, Dayna

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Wildly ramified Galois representations and a generalization of a conjecture of Serre.

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The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead...

Dihedral Galois representations and Katz modular forms.

Wiese, Gabor (2004)

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Infinitely ramified Galois representations.

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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, $p$ -adic Galois representations associated to holomorphic Hilbert modular newforms.

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This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over $ℚ$ ? Let $ℓ$ be a prime and $t$ a positive integer. We show that that the finite simple groups of Lie type $B_{n} (ℓ^{k}) = 3 D S O_{2 n + 1} {(𝔽_{ℓ^{k}})}^{d e r}$ if $ℓ \equiv 3, 5 (mod 8)$ and $G_{2} (ℓ^{k})$ appear as Galois groups over $ℚ$ , for some $k$ divisible by $t$ . In particular, for each of the two Lie types and fixed $ℓ$ we construct infinitely many Galois groups but we do not have a precise...

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Displaying similar documents to “ SL 3 ( 𝔽 2 ) -extensions of ℚ and arithmetic cohomology modulo 2.”

Displaying similar documents to “ ${SL}_{3} (𝔽_{2})$ -extensions of $ℚ$ and arithmetic cohomology modulo 2.”