p −1-Linear Maps in Algebra and Geometry

By Manuel Blickle, Karl Schwede. 2012

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e2f68eaaf4f6c95ab3d8fe83890a1cf9eca4160b

Citations in the corpus

• F-signature and Hilbert–Kunz multiplicity : a combined approach and comparison (2016, unknown): “In particular, the first proof of Theorem 5.1 gives a readily computable lower bound for the F -signature of a strongly F -regular ring.”