The formal model of the Igusa Sample Clauses

The formal model of the Igusa tower In order to define the formal model of the Igusa tower in this case, we cannot simply follow the discrete case verbatim: Normality of formal schemes is problematic in the non- Noetherian case, and excellence is definitely not satisfied. Instead, we opt for a definition by base-change, a basic strategy which we shall often use in the following: Like before, let 0 ≤ ϵ ∈ log |K| and fix an element tє ∈ K with |tє| = |t|є. Then there is a unique morphism ι : Fp[[t]] → R sending t '→ tє, which gives rise to an embedding Fp((t)) ‹→ K. In other words, we now consider two different copies of Fp((t)) inside K. Since by definition, X′(ϵ) = X′(|Ha| ≥ |tє|), we can now reinterpret X′(ϵ) as the base change of XF′p((t))(1) along ι : Fp((t)) → K. This is the reason we allowed r = −1 in the last section. We also obtain a canonical formal model by base-changing X′Fp[[t]](1):
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