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Fix error.
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HechtiDerLachs committed May 15, 2023
1 parent 883922d commit f1919ba
Showing 1 changed file with 39 additions and 0 deletions.
39 changes: 39 additions & 0 deletions src/AlgebraicGeometry/Schemes/Methods.jl
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@doc raw"""
base_change(phi::Any, X::Scheme)
For a `Scheme` ``X`` over a `base_ring` ``𝕜`` and a map ``φ : 𝕜 → R``
we compute ``X' = X ×ₖ Spec(R)`` and return a pair `(X', f)` where
``f : X' → X`` is the canonical morphism.
!!! note
We do not restrict `phi` to be a `Hecke.Map` so that one can also use
coercion, anonymous functions, etc.
"""
function base_change(phi::Any, X::Scheme)
error("base_change not implemented for input of type $(typeof(X))")
end

@doc raw"""
base_change(phi::Any, f::SchemeMor;
domain_map::SchemeMor, codomain_map::SchemeMor
)
For a morphism ``f : X → Y`` with both ``X`` and ``Y`` defined over a
`base_ring` ``𝕜`` and a map ``φ : 𝕜 → R`` return a triple `(a, F, b)`
where ``a : X' → X`` is the morphism from `base_change(phi, X)`,
``b : Y' → Y`` the one for ``Y``, and ``F : X' → Y'`` the induced
morphism on those fiber products.
!!! note
We do not restrict `phi` to be a `Hecke.Map` so that one can also use
coercion, anonymous functions, etc.
!!! note
The morphisms ``a`` and ``b`` can be passed as the optional arguments
`domain_map` and `codomain_map`, respectively.
"""
function base_change(phi::Any, f::SchemeMor;
domain_map::SchemeMor, codomain_map::SchemeMor
)
error("base_change not implemented for input of type $(typeof(f))")
end

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