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Mathoverflow.net news digest

  • 0 days

    Ramsey ultrafilters after adding splitting reals

    This is a reference request. Are there any results of the following kind?
    Assume $\mathrm{CH}$ and let $\mathcal{U}$ be a Ramsey ultrafilter. Let $c$ be a Cohen real. Then in $V[c]$, can $\mathcal{U}\cup\{c\}$ be extended to a Ramsey ultrafilter again? Instead of a Cohen real, any results concerning other splitting reals would...

  • 0 days

    Robin’s inequality and extremal σ(n)/n: Has a “no-arbitrage” or supermartingale ...

    Background.Robin’s theorem (1984) states that the Riemann Hypothesis is equivalent to the inequality
    σ(n)<eγnlog⁡log⁡nfor alln
    5040,σ(n)<eγnloglognfor all n>5040,whereσ(n)σ(n) is the sum-of-divisors function andγγ is the Euler–Mascheroni constant.​It is also known that any least counterexample, if it exists, must lie among certain extremal sequences such as superabundant...

  • 0 days

    Reference request: Integral motivic cohomology of $BG$

    Are there references that compute the integral motivic cohomology $\mathrm{H}^{p,q}(BG,\mathbb Z)$, for $G$ finite cyclic and where $BG$ is defined over the rationals.
    I am particularly interested in $G=\mu_2$.
    Thanks in advance!

  • 2 days

    On iterated adic completions. Does $(M^{\wedge I})^{\wedge J}\cong M^{\wedge I+J...

    $\def\C{\mathrm{C}}\def\P{\mathrm{P}}\def\AR{\mathrm{AR}}$(All rings are commutative and unital.) I am trying to prove or disprove the following:
    ($\C$). Iterated adic completion amounts to joint adic completion. More precisely: Let $R$ be a ring and $a_1,\dots,a_n\in R$. Suppose $M$ is an $R$-module. Define $M_0=M$ and $M_i=M^{\wedge a_i}_{i-1}$, $i=1,\dots,n$. Then $M_n\cong M^{\wedge\mathfrak...

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