# All Questions

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### If an abelian category $\mathcal{A}$ has enough injectives then so is $\mathrm{Ch}^{\geq 0}(\mathcal{A})$

Well my question is as clear as its title suggests. So here I would like to clarify on the fact that an object $A^\cdot$ in $\mathrm{Ch}^{\geq 0}(\mathcal{A})$ is injective if and only if ...
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### An example of optimal control for linear case [on hold]

Does someone have an example of optimal control for the linear case?
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### $\delta$-functor and commutativity of pull-back with right derivation

Let $f:X \to Y$ be a faithfully flat projective morphism of noetherial $\mathbb{C}$-schemes. Assume that $Y$ is affine, smooth over $\mathbb{C}$. Let $y \in Y$ be a closed point with residue field, ...
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### Is this one of the solutions for the problem: $\ a^3 + b^3 = c^3\$ has no nonzero integer solutions? [on hold]

Let $\ a^3 + b^3 = c^3,\ a, b, c \in \mathbb Z^*,\$we can assume that all variables are coprime. Because $c^3 - b ^ 3 = (c - b)((c - b) ^ 2 + 3cb)= a ^ 3,\$ so $\ (c - b)\$ is factor of $a$, let ...
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### Hypersurfaces with rational self-maps

I'm looking for interesting examples of hypersurfaces $X\subset \mathbb P^n$ with a rational self-map $X\dashrightarrow X$? Are there such examples for cubic hypersurfaces?
Let $S$ be a smooth cubic surface defined by $f\in \mathbb Q[x,y,z,w]$. Is there an algorithm to write down the 27 lines on $S$? Or at least find a field extension of $\mathbb Q$ over which these ...