Morphisms of schemes arenot determined by their underlying map of points.
34909
To what extent is a scheme morphism determined by its topological map?
132571
Local homeomorphisms which are not covering map?
149973
Showing the following coordinate rings are not isomorphic
9204
Counterexamples to the avoidance lemma for arbitrary ideals
97114
Square is not an algebraic set.
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
67383
Prove that $G'$ is not planar.
148007
Is the pushforward of the sheaf of differentials on an elliptic curve over a scheme necessarily trivial?
129288
proof that topologist sine curve is not locally connected
24828
surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
35115
Questions on how to prove that a set of connectives is NOT functionally complete
25874
Showing that a certain map is not flat by explicit counterexample
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
12405
Topologist's sine curve is not path-connected
98696
Is the exponential map ever not injective?
153984
The direct image of an ideal need not be an ideal