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p −1-Linear Maps in Algebra and Geometry

In: Commutative Algebra

Author

Listed:
  • Manuel Blickle

    (Johannes Gutenberg-Universität Mainz, Institut für Mathematik)

  • Karl Schwede

    (The Pennsylvania State University, Department of Mathematics)

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.

Suggested Citation

  • Manuel Blickle & Karl Schwede, 2013. "p −1-Linear Maps in Algebra and Geometry," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, edition 127, pages 123-205, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5292-8_5
    DOI: 10.1007/978-1-4614-5292-8_5
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