Is there an isomorphism $f_*\mathcal{H}om_{\mathcal{O}_X}(f^*\mathcal{G},\mathcal{F}) \cong \mathcal{H}om_{\mathcal{O}_Y}(\mathcal{G},f_*\mathcal{F})$

score 309 · Answer 11 · 2026-02-23 14:11:25

309

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Two possible definitions of composition of morphisms of ringed spaces. Are they equivalent?

Published on 23 Feb 2026 - 14:11

score 195 · Answer 12 · 2026-02-23 14:13:18

Formally smooth morphism of formal schemes $\mathfrak X \to\mathfrak Y$ induces formally smooth morphisms of schemes $\mathfrak X_n \to\mathfrak Y_n$?

score 70 · Answer 13 · 2026-02-23 14:09:45

70

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Why there is no notion ´bijective´ regarding morphism of schemes?

Published on 23 Feb 2026 - 14:09

score 101 · Answer 14 · 2026-02-23 14:11:51

101

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The spectrum of a ring minus a prime of height $1$

Published on 23 Feb 2026 - 14:11

score 180 · Answer 15 · 2026-02-23 14:11:12

180

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Characterisation isomorphisms of ringed spaces: $(f,f^\flat)$ iso iff $(f,f^\sharp)$ iso?

Published on 23 Feb 2026 - 14:11

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Liu's Algebraic Geometry Ex 2.12

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Exercise 3.10 from Hartshorne

Is there an isomorphism $f_\mathcal{H}om_{\mathcal{O}_X}(f^\mathcal{G},\mathcal{F}) \cong \mathcal{H}om_{\mathcal{O}_Y}(\mathcal{G},f_*\mathcal{F})$

Two possible definitions of composition of morphisms of ringed spaces. Are they equivalent?

Formally smooth morphism of formal schemes $\mathfrak X \to\mathfrak Y$ induces formally smooth morphisms of schemes $\mathfrak X_n \to\mathfrak Y_n$?

Why there is no notion ´bijective´ regarding morphism of schemes?

The spectrum of a ring minus a prime of height $1$

Characterisation isomorphisms of ringed spaces: $(f,f^\flat)$ iso iff $(f,f^\sharp)$ iso?

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