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What is the restriction of a deformation?

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#definition #schemes #deformation-theory
574
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Quasi coherent sheaves restricted to affine open subsets

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#algebraic-geometry #schemes #affine-schemes #quasicoherent-sheaves
849
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Correspondence between fractional ideals of $K$ and invertible sheaves of $\operatorname{Spec}\mathcal O_K$.

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#algebraic-geometry #algebraic-number-theory #schemes
398
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Closed subschemes as subsets

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#algebraic-geometry #schemes
2.1k
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Quasi separated scheme

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#algebraic-geometry #schemes
695
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Morphisms of global sections and Morphisms of Schemes

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#algebraic-geometry #schemes
800
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Let $X$ be a connected scheme. Then $X$ irreducible iff $\forall x, \text{ Spec}(\mathcal{O}_{X,x})$ is

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#general-topology #algebraic-geometry #schemes #affine-schemes
260
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Open subset associated to a global section of a scheme

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#algebraic-geometry #schemes #affine-schemes
75
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Closed subschemes in closed subschemes

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#sheaf-theory #schemes
217
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Property of étale morphisms

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#algebraic-geometry #schemes
173
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$X$ is a scheme over $k$. Considering the map $f:X\to k$

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#algebraic-geometry #schemes
677
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Epimorphisms in the category of separated schemes

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#algebraic-geometry #category-theory #schemes #separation-axioms
37
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Given a family of schemes $\pi:X \to B$ which is generically smooth how can I find the singular locus $B_{sing}$?

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#algebraic-geometry #schemes
419
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Are elements of a ring actual functions or sections on the spectrum?

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#algebraic-geometry #schemes #affine-schemes
451
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Intuitive reason why irreducible fibre of same dimension implies irreducibility

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#algebraic-geometry #schemes #projective-schemes

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