arxiv: 1205.4577 · v2 · pith:CVFCKYG7new · submitted 2012-05-21 · 🧮 math.AG · math.AC

p⁻¹-linear maps in algebra and geometry

Manuel Blickle , Karl Schwede This is my paper

classification 🧮 math.AG math.AC

keywords linearalgebramapsmodulesapplicationsarticlebasiccharacteristic

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In this article we survey the basic properties of $p^{-e}$-linear endomorphisms of coherent $\O_X$-modules, i.e. of $\O_X$-linear maps $F_* \sF \to \sG$ where $\sF,\sG$ are $\O_X$-modules and $F$ is the Frobenius of a variety of finite type over a perfect field of characteristic $p > 0$. We emphasize their relevance to commutative algebra, local cohomology and the theory of test ideals on the one hand, and global geometric applications to vanishing theorems and lifting of sections on the other.

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p⁻¹-linear maps in algebra and geometry

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