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Why is the ring of local-ring valued points of a ring scheme a local ring.

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#algebraic-geometry #schemes #algebraic-groups #representable-functor #ringed-spaces
2.9k
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Definition of smooth manifold using sheaves.

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#differential-geometry #manifolds #smooth-manifolds #sheaf-theory #ringed-spaces
174
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Is the adjunct of the comorphism for a closed immersion of ringed spaces an isomorphism?

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#differential-geometry #algebraic-geometry #sheaf-theory #ringed-spaces
709
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Stalks and closed immersion

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#algebraic-geometry #sheaf-theory #ringed-spaces
40
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The radical presheaf is not a sheaf

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#sheaf-theory #ringed-spaces
45
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Locally, every coherent sheaf is isomorphic to the cokernel of a homomorphism $\phi: \mathcal{A}^q \to \mathcal{A}^p$

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#algebraic-geometry #sheaf-theory #ringed-spaces
100
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On a ringed space: If a section has zero germ at $x$, must it be zero on some neighborhood of $x$?

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#reference-request #sheaf-theory #ringed-spaces
34
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"Punctured stalk" of a locally ringed space (at a closed point) is the fraction field of the stalk?

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#sheaf-theory #ringed-spaces
51
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Do restrictions preserve ring structure of ringed space?

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#algebraic-geometry #sheaf-theory #schemes #ringed-spaces
162
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Is there a morphism of ringed spaces between smooth (resp., complex) manifolds that is not local?

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#smooth-manifolds #complex-geometry #sheaf-theory #ringed-spaces
120
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Subvarieties of an abstract affine variety

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#algebraic-geometry #sheaf-theory #affine-varieties #ringed-spaces
66
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Spectrum is ringed space

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#algebraic-geometry #reference-request #schemes #ringed-spaces
116
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Characterization of isomorphisms of ringed spaces

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#sheaf-theory #ringed-spaces
54
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More examples of morphisms of ringed spaces that aren't local?

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#algebraic-geometry #examples-counterexamples #affine-schemes #ringed-spaces
51
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Existence of a sheafification for every presheaf $ \mathcal{O} '$

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#sheaf-theory #ringed-spaces #supermanifolds #presheaves

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