F-Split and F-Regular Varieties with a Diagonalizable Group Action

Piotr Achinger, Nathan Owen Ilten, Hendrik Süß

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    Abstract

    Let H be a diagonalizable group over an algebraically closed field
    k of positive characteristic, and X a normal k-variety with an H-action. Under
    a mild hypothesis, e.g. H a torus or X quasiprojective, we construct a certain
    quotient log pair (Y,Δ) and show that X is F-split (F-regular) if and only
    if the pair (Y,Δ) if F-split (F-regular). We relate splittings of X compatible
    with H-invariant subvarieties to compatible splittings of (Y,Δ), as well as
    discussing diagonal splittings of X. We apply this machinery to analyze the
    F-splitting and F-regularity of complexity-one T-varieties and toric vector
    bundles, among other examples
    Original languageEnglish
    Pages (from-to)1534-7486
    JournalJournal of Algebraic Geometry
    Volume26
    Issue number0
    DOIs
    Publication statusPublished - 9 Dec 2016

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