Counterexamples in the theory of coherent sheaves
129929
"sheaves of germs of differentiable functions are by no means coherent"?
138298
Learning about Grothendieck's Galois Theory.
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
8654
Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.
81550
Linking two theorems: on algebraic closure and on minimal splitting field
123132
Counterexample for a non-measurable function?
140003
Why only consider Dolbeault cohomology?
102879
$\operatorname{Ext}$ and injectives, respectively projectives
43626
Open Mapping Theorem: counterexample
61926
Why are Grothendieck's and Hartshorne's definitions of quasi-coherence equivalent?
53531
Birational and faithfully flat $\implies$ isomorphism
114773
counterexamples on modules
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
76563
Category Theory usage in Algebraic Topology
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
22529
The support of a non finitely generated module
76432
$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.