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Is $A[[x_1,x_2,\dots]]$ flat over $A[x_1,x_2,\dots]$? ($A$ noetherian and commutative)

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#commutative-algebra #formal-power-series #flatness #polynomial-rings
35
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Can we deduce the exactness of the pervious modules sequence if the localized exact modules sequence is exact?

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#homological-algebra #exact-sequence #flatness
198
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are the global sections of a flat sheaf over a discrete valuation ring a free module?

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#algebraic-geometry #schemes #sheaf-cohomology #coherent-sheaves #flatness
124
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The flat module, module is not flat

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#modules #flatness
81
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Tower of ring extensions and flatness

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#abstract-algebra #ring-theory #commutative-algebra #flatness
119
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Prove that if $M$ is flat over $R$ and $N$ is flat over $S$ then $M\otimes N$ is flat over $S$

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#modules #flatness
177
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Is every local flat extension of a DVR a domain?

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#algebraic-geometry #ring-theory #commutative-algebra #dedekind-domain #flatness
67
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Module not flat

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#modules #flatness
47
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At which point does a sphere's edges look flat?

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#geometry #flatness
90
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Condition for a finitely generated flat module be projective

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#modules #projective-module #finitely-generated #flatness
325
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Relative Bertini theorem

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#algebraic-geometry #divisors-algebraic-geometry #flatness #projective-schemes
374
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How to prove that a morphism is flat

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#algebraic-geometry #flatness #deformation-theory
211
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Flat $\mathbb{Z}$-modules and algebraic independence

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#abstract-algebra #commutative-algebra #homological-algebra #flatness #transcendence-theory
421
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On faithfully flat and faithfully projective modules

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#commutative-algebra #modules #homological-algebra #projective-module #flatness
38
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Flatness ascends up a inverse system

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#algebraic-geometry #commutative-algebra #flatness

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