Hecke operators‌ Sample Clauses

Hecke operators‌. 2.5.1 The tame Hecke algebra For any l ∈ N coprime to Np, the Hecke operator T5 on modular forms can be defined as usual using Hecke correspondences. To spell this out, let us focus for simplicity on the case that l is a prime. Consider the perfectoid modular curve n XΓ(p∞)×Γ0(5) = XΓ(p∞) ×X XΓ0(5) ∼ lim− XΓ(pn)×Γ0(5). The maps π1,2 : XΓ0(5) → X given by π1 : (E, G) '→ E and π2 : (E, G) '→ E/G, respectively, restrict to π1,2 : XΓ0(5)(ϵ) → X (ϵ) and induce Cartesian squares XΓ(p∞)(ϵ)a XΓ0(p)(ϵ)a π2,∞ π2 XΓ(p∞)×Γ0(5)(ϵ)a XΓ0(p)×Γ0(5)(ϵ)a π1,∞ π1 XΓ(p∞)(ϵ)a = π1∗ω n XΓ0(p)(ϵ)a. Γ0(p)
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