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Displaying similar documents to “On the Structure of Commutative Affine Group Schemes over a Non-Perfect Field.”

The set of points at which a morphism of affine schemes is not finite

Zbigniew Jelonek, Marek Karaś (2002)

Colloquium Mathematicae

Similarity:

Assume that X,Y are integral noetherian affine schemes. Let f:X → Y be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism f is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

Similarity:

Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

Similarity:

An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.