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### Weaker versions of Gandy ordinals

Gostanian's paper "The next admissible ordinal" (see https://www.sciencedirect.com/science/article/pii/0003484379900251 ), is concerned with the supremum of the $\alpha$-recursive ordinals for various ...
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### For non-noether $A$, there exists a complex $L^\bullet$ such that for all $M$ $H^i(X, \mathscr{F} \otimes_A M) \cong h^i(L^\bullet \otimes_A M)$

Let $A$ be a ring, $X \to A$ a proper morphism of finite presentation, and $\mathscr{F}$ be a quasi-coherent module on $X$ of locally finitely presented, which is flat over $A$. Then there exists a ...
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### When are extensions of algebraically good groups algebraically good?

Let $G$ be a discrete group. The pro-algebraic completion of $G$ is a pro-algebraic group $G^{\mathrm{alg}}$ together with a morphism $s:G\to G^{\mathrm{alg}}$ which is initial among all morphisms ...
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### Optimization of an integral functional when the multiplier rule yields no useful information

Let $(E,\mathcal E,\lambda)$ be a measure space $\mu\ll\lambda$ be a probability measure on $(E,\mathcal E)$ $p\in[1,\infty)$ $k\in\mathbb N$ $f:E\times\mathbb R^k\times\mathbb R^k\to[0,\infty)$ such ...
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### Anti-holomorphic involutions of a complex linear algebraic group

Let $G$ be a connected linear algebraic group over the field of complex number ${\Bbb C}$. Let $G({\Bbb C})$ denote the complex Lie group of ${\Bbb C}$-points of $G$. Let $\sigma$ be an anti-...
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### Index and congruence subgroup from scaling variables of Jacobi form

Let $J_{k,m}(N)$ be the space of Jacobi forms of weight $k$, index $m$, and congruence subgroup $\Gamma_{0}(N) \rtimes \mathbb{Z}^{2}$. I do not believe it is relevant here to specify what type of ...
Let $M\subset B(\mathcal{H})$ be an infinite dimensional vN algebra in standard form. Fix $\xi\neq 0 \in \mathcal{H}$, does there exist $M\ni x_{\xi}\neq I$ such that $x_{\xi}(\xi)=\xi$?