All Questions
Tagged with flatness reference-request
7 questions with no upvoted or accepted answers
8
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Classification of flat Riemannian three manifold
By a theorem of L. Bieberbach we know that that every closed flat Riemannian manifold is a quotient of a torus via action of a finite group $\Gamma$. In this question we are interested in the ...
- 1,915
6
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Flat base change in the complex analytic setting
On page 255 of Hartshorne's Algebraic Geometry, it is shown that "cohomology commutes with flat base extension":
Proposition III.9.3: Let $f : X \to Y$ be a separated morphism of finite type of ...
- 61
3
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214
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Representability of Flattening stratification functor
Let $f:X \to Y$ be a projective morphism between noetherian scheme. Is there any know condition under which there exists a functorial stratification of $Y$ i.e., there exists a filtration by locally ...
- 1,981
2
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Ultraproducts and subobjects of projectives
Usually the question whether the class of projective algebras in a given variety is closed under taking subalgebras seems to be quite hard. In varieties with well understood dual geometry (e. g. ...
- 18.4k
1
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191
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Deformation of projective bundles
Let $\pi:\mathcal{X} \to \mathbb{P}^1$ be a flat, projective family of noetherian schemes with generic fiber a smooth, projective variety. Let $p:\mathcal{Y} \to \mathcal{X}$ be another flat, ...
- 2,126
0
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Fiberwise injective resolution of coherent sheaf
Let $k$ be an algebraically closed field (of characteristic zero) and $X, Y$ be projective $k$-varieties. Let $F$ be a coherent sheaf on $X \times_k Y$, flat over $Y$. Does there exists a coherent $\...
- 2,323
0
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Is the $B$-tensor power of flat $A$-modules, $A$-flat?
Let $k$ be an algebraically closed field and $A, B$ be two finitely generated $k$-algebras. Suppose $B$ is flat over $A$. Let $M$ be a finitely generated $B$-module which is flat over $A$. Is it true ...
- 1,981