p −1-Linear Maps in Algebra and Geometry

Manuel Blickle () and Karl Schwede ()
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Manuel Blickle: Johannes Gutenberg-Universität Mainz, Institut für Mathematik
Karl Schwede: The Pennsylvania State University, Department of Mathematics

A chapter in Commutative Algebra, 2013, pp 123-205 from Springer

Abstract: Abstract At least since Habousch’s proof of Kempf’s vanishing theorem, Frobenius splitting techniques have played a crucial role in geometric representation theory and algebraic geometry over a field of positive characteristic. In this article we survey some recent developments which grew out of the confluence of Frobenius splitting techniques and tight closure theory and which provide a framework for higher dimension geometry in positive characteristic. We focus on local properties, i.e. singularities, test ideals, and local cohomology on the one hand and global geometric applicatioms to vanishing theorems and lifting of sections on the other.

Keywords: Line Bundle; Finite Type; Coherent Sheaf; Local Cohomology; Projection Formula (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-5292-8_5

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DOI: 10.1007/978-1-4614-5292-8_5

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