Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective Mathlib.AlgebraicGeometry.Morphisms.Immersion Mathlib.AlgebraicGeometry.Morphisms.Separated Mathlib.AlgebraicGeometry.RationalMap Mathlib.AlgebraicGeometry.ValuativeCriterion Mathlib.AlgebraicGeometry.PullbackCarrier Mathlib.AlgebraicGeometry.Morphisms.Universally...
This leads to set and develop basic notions on ringed finite spaces and morphisms, as being affine, schematic, semi-separated, etc, focusing on its cohomological properties. Finally, we see how to embed the category of quasi-compact and quasi-separated schemes in a localization of the ...
Finally, we construct a fully faithful and essentially surjective functor from a localization of a full subcategory of the category of schematic finite spaces and schematic morphisms to the category of quasi-compact and quasi-separated schemes. 展开 关键词:...
is a pair T = (Σ, I) where Σ is a signature and I a class of Σ-interpretations, the models of T , that is closed under variable reassignment (i.e., every Σ-interpretation that differs from one in I only for how it interprets the variables is also in I) and iso- morphism....
Furthermore, for eachx\le y, since the continuous image of a connected topological space is connected, the morphism\varphi _{xy}induces a unique ring homomorphismA_x^{\alpha _i}\rightarrow A_y^{\beta _j}for every\beta _j\in \pi ^{-1}(y)and\alpha _i=\varphi _{xy}(\beta _j...
Moreover, the orbit of e under L (or R) consists of the evaluation morphisms at all points of G. Therefore both [Math Processing Error] and [Math Processing Error] separate points in [Math Processing Error], so that [Math Processing Error] by the Urysohn lemma. A version of [17, ...
Finally, we construct a fully faithful and essentially surjective functor from a localization of a full subcategory of the category of schematic finite spaces and schematic morphisms to the category of quasi-compact and quasi-separated schemes....
and a decreasing, separated, exhaustive filtration of the K-vector space DK=(D⊗K0nrK¯)GK by K-vector subspaces FiliDK. These are the objects of a pre-abelian category MF(ϕ,N,GK). (It is not an abelian category, since morphisms may not be strictly compatible with the filtration...
Letkbe a field,Ga smoothk-group scheme of finite type, andXa quasi-compact quasi-separated locally KrullG-scheme. Assume that there is ak-schemeZof finite type and a dominantk-morphismZ→X. Letφ:X→Ybe aG-invariant morphism such thatOY→(φ⁎OX)Gis an isomorphism. ThenYis locally ...