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Stack semantics for the layman

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#logic #category-theory #sheaf-theory #quantifiers #topos-theory
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Sheaf of regular functions

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#algebraic-geometry #sheaf-theory
5.4k
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Adjunction of pushforward and pullback

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#abstract-algebra #algebraic-geometry #sheaf-theory #quasicoherent-sheaves
197
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Morphisms of schemes are $\mathcal{O}-$modules

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#algebraic-geometry #sheaf-theory #schemes
415
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Checking quasicoherence on a qcqs scheme

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#abstract-algebra #algebraic-geometry #commutative-algebra #sheaf-theory #quasicoherent-sheaves
508
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$\phi:\mathcal F\rightarrow \mathcal G$ is an isomorphism if there is an open cover on which $\phi(U)$ is an isomorphism.

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#algebraic-geometry #sheaf-theory
285
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Turning a geometric vector bundle into a free $\mathscr{O}_X$-module

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#algebraic-geometry #sheaf-theory #vector-bundles #quasicoherent-sheaves
7.1k
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Canonical sheaf projective bundle

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#algebraic-geometry #sheaf-theory #vector-bundles #exact-sequence #divisors-algebraic-geometry
277
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Vanishing of Tor sheaf on a union of subschemes with vanishing Tor.

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#algebraic-geometry #homological-algebra #sheaf-theory #schemes
2.4k
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What does it mean for a sequence of sheaves to be exact

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#algebraic-geometry #sheaf-theory
327
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Sheafyness and relative chinese remainder theorem

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#algebraic-geometry #commutative-algebra #sheaf-theory #schemes #chinese-remainder-theorem
2.6k
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Stalks and direct image

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#algebraic-geometry #sheaf-theory
1.4k
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Definition of a morphism of locally ringed spaces

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#algebraic-geometry #sheaf-theory #ringed-spaces
263
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Description of generated Grothendieck topology

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#algebraic-geometry #category-theory #sheaf-theory #topos-theory #grothendieck-topologies
370
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Pushforward of a quasicoherent sheaf on a noetherian scheme is quasicoherent

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#algebraic-geometry #sheaf-theory #schemes #quasicoherent-sheaves

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