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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
4
votes
Important (interesting) unsolved problems
The big open problem around where I work (D-modules) is the Jacobian Conjecture. This states that if you have an algebraic map f from C^n to C^n whose jacobian determinant is a non-zero constant, the …
3
votes
When does the converse to Schur's Lemma hold?
Let $p$ be a prime, and let $R(p)$ be the residue field at $p$. If $R \to R(p)$ is not a surjection, then then $R(p)$ is an $R$ module whose endomorphism ring is $R(p)$, but such that the image of $R …