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Mathoverflow.net news digest

  • 0 days

    A Baire Boolean ring of size $\omega_1$ without SCP?

    I am interested in the following Boolean-ring question, motivated by a renorming problem for Banach spaces of density $\omega_1$.
    Let $\mathfrak A$ be a Boolean ring, not necessarily with a maximal element. I shall write $a\leq b$ when $ab=a$. For $a,i\in\mathfrak A$, put...

  • 0 days

    Can $\gcd(n^k \pm 1, \hspace{2mm} n! \pm 1)>1$ have arbitrarily many but finitel...

    Fix an integer $k \geq 2$ and let $n \geq 2$ be integer as well. Let $\lambda_1,\lambda_2 \in \{-1, 1 \}$, and then consider the set$$S_{k}^{\lambda_1,\lambda_2}:= \{n \in \mathbb{N}\setminus\{0,1\} : \gcd(n^k+\lambda_1, \hspace{2mm} n!+\lambda_2) &...

  • 0 days

    Constant sheaf functor to the etale topos

    Let $X$ be a connected scheme. Remark 4.2.14 from Bhatt-Scholze "The pro-etale topology for schemes" states that the constant sheaf functor $\mathop{\rm Set}\to \mathop{\rm Shv}(X_{et})$ is not always limit-preserving. Is there an example of the failure...

  • 7 days

    The evaluation of a multi-parameter binomial sum involving harmonic numbers

    I have been working on finding exact, closed-form discrete evaluations for a specific family of combinatorial sums, aiming to find exact identities where standard asymptotic or continuous approximations are typically used.
    Through this work, I have found an identity. For $a > 1$, $b \le c$, and $d \ge 0$:...

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