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Difficulty understanding Hartshorne Theorem IV.4.11

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#algebraic-geometry #elliptic-curves #flatness
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Flat modules over a PID

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#abstract-algebra #modules #projective-module #flatness #free-modules
121
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Submodule of a flat module.

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#commutative-algebra #flatness
965
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When an integral extension of integral domains is flat?

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#commutative-algebra #integral-domain #flatness
66
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When flat submodule is direct summand?

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#abelian-groups #flatness
464
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Flatness in a short exact sequence. If the

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#homological-algebra #tensor-products #exact-sequence #flatness #functors
605
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Localization and flatness

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#commutative-algebra #localization #flatness
103
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Computing $\operatorname{Tor}^R_1(M,N)$

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#commutative-algebra #tensor-products #projective-module #flatness
124
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Does flatness ascend through a free ring map?

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#commutative-algebra #flatness #free-modules
650
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Can it be that $R[[x]]$ is flat over $R$ but not over $R[x]$?

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#ring-theory #commutative-algebra #flatness
373
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If $M$ is a flat $R$-module and $rm=0$ for some $r$ and $m$, show $m=0$.

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#commutative-algebra #tensor-products #flatness
138
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If $A\subset B$ are integral domains with the same field of fractions and $B$ is faithfully flat over $A$, then $A=B$.

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#ring-theory #commutative-algebra #flatness
1k
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Projective and flat vs. faithfully flat

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#commutative-algebra #modules #tensor-products #projective-module #flatness
83
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Isomorphisms in faithfully flat $R$-modules

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#modules #tensor-products #flatness
967
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Why does a flat finite type morphism of irreducible noetherian schemes map generic pt to generic pt

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#algebraic-geometry #commutative-algebra #schemes #flatness

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