tl» Sample Clauses

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tl» s for l - pN. Then we have a homomorphism T˜Z → Fp defined by sending Tl → Tr ρ(Frobl). Denote the kernel of this homomorphisms by mρ. Simi- larly, we get an ideal mρ of T˜Fp := T˜Z bZ Fp defined again as the kernel of the map evaluating the Hecke operators at the traces of Xxxxxxxxx. Since the image of these homomorphisms are finite subrings of an integral do- main, hence a field, the ideals mρ and mρ will be maximal. We will say that a maximal ideal in a Hecke-module is Xxxxxxxxxx if the associated Galois representation is reducible. A Hecke-module is Xxxxxxxxxx if all the maximal ideals in its support are Xxxxxxxxxx. For simplicity we will assume N > 4 so that Γ1(N ) is sufficiently small (see [DI95, §12.1]) and sometimes we will denote this group simply by X. Definition 2.2.3. We will say that ρ is cohomologically modular of weight k ě 2 and level N if 1 p mρ H1(Γ (N ), Symk´2F2) ‰ 0. We begin with the following lemma which shows that it does not matter whether our rings are defined over Fp or Fp. The proof of the lemma is just standard commutative algebra. Lemma 2.2.4. For k ě 2 and Γ := Γ1(N ), we have that H1(Γ, Symk´2F2) ‰ 0 if and only if p mρ p ρ H1(Γ, Symk´2F2)m ‰ 0. Proof. Since (p) Ă AnnT˜Z `H (Γ, Sym F )˘ , without loss of gener-
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Related to tl»

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  • Project Description In two or three brief sentences, provide a concise description of your exhibition. Include the subject matter, type of objects to be included (paintings, sculpture, manuscripts, etc.), those responsible for organizing the exhibition, and catalogue author(s).

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