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Mathoverflow.net news digest

  • 0 days

    On the proof of Weil conjectures in the curve case

    I'm struggling to understand an argument in the book "Weil Conjectures, Perverse Sheaves, and $l$-adic Fourier Transform" by Kiehl and Weissauer.
    In Theorem I.6.1, they prove (in specific cases) that the $i$-th cohomology of a pure sheaf of weight $w$ has weight $w+i$. I'm confused by their argument on the second half of page $47$ where they treat the special case of a geometrically constant sheaf...

  • 0 days

    Is there a standard name for vertex partitioning via ordered, successive neighbo...

    Let $G=(V,E)$ be a finite graph together with a fixed total ordering of its vertices. Consider the following greedy procedure.
    Let $R_0=V$. At step $k$, choose the first vertex $r_k \in R_k$ in the prescribed order. Form the block:
    $$B_k = N[r_k] \cap R_k$$...

  • 0 days

    Confusion on the immersion theorem of Lees and Lashof

    I have a question about a definition in the immersion theorem of Lees and Lashof: in Lashof's paper "The immersion approach to triangulation and smoothing" he proves that the differential map from the space of immersions of an open manifold to the space...

  • 0 days

    Morphisms of locales whose dissolution is open

    Recall that a morphism $f\colon X\to Y$ of locales is said to be open when its inverse image part $f^*\colon \mathcal{O}(Y) \to \mathcal{O}(X)$ (where $\mathcal{O}(X)$ denotes the frame of opens which defines the locale $X$) has a left adjoint $f_!\colon...

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