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15
77
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Image of rational points of a morphism (defined over $\mathbb{Q}$) between affine spaces

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#algebraic-geometry #rational-numbers #affine-geometry #affine-varieties
188
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Clopen sets in affine space

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#algebraic-geometry #affine-varieties
172
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Going from varieties to schemes

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#algebraic-geometry #schemes #affine-schemes #affine-varieties #zariski-topology
100
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Algebraic de Rham cohomology of the affine plane in characteristic p?

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#reference-request #differential-forms #affine-varieties #de-rham-cohomology #positive-characteristic
60
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Showing the following subset is an affine variety

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#algebraic-geometry #polynomials #affine-varieties
494
Views

Schemes and Varieties

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#algebraic-geometry #schemes #affine-schemes #affine-varieties
53
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Is a Locally Affine Ringed Space Noetherian?

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#algebraic-geometry #commutative-algebra #sheaf-theory #affine-varieties
120
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Irreducible algebraic sets vs varieties

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#algebraic-geometry #affine-varieties
208
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Let $I=(y^2-x^2,y^2+x^2)$. Find $V(I)$ and $\text{dim}_{\mathbb{C}}(\mathbb{C}[x,y]/I)$

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#algebraic-geometry #polynomials #algebraic-curves #affine-varieties
72
Views

$S(X)\simeq S(Y) \Leftrightarrow X\simeq Y$?

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#algebraic-geometry #projective-geometry #affine-varieties
164
Views

Bijection: Morphisms of algebraic sets and morphisms of coordinate rings

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#algebraic-geometry #affine-varieties
114
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Regular functions on affine varieties

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#algebraic-geometry #commutative-algebra #localization #affine-schemes #affine-varieties
650
Views

A variety $X$ is irreducible $\iff I(X)$ is prime

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#commutative-algebra #roots #maximal-and-prime-ideals #affine-varieties
136
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Suppose $ g$ has the property that if $f(x)≠0$, then $g(x)=0$. Then prove that $g(x)=0$ for all $x$.

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#abstract-algebra #polynomials #ring-theory #integral-domain #affine-varieties
151
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Dimension of Intersection of Algebraic Sets

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#algebraic-geometry #commutative-algebra #affine-varieties

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