Abstract
In this paper we study singularities defined by the action of Frobenius in characteristic . We prove results analogous to inversion of adjunction along a center of log canonicity. For example, we show that if is a Gorenstein normal variety then to every normal center of sharp -purity such that is -pure at the generic point of , there exists a canonically defined -divisor on satisfying . Furthermore, the singularities of near are “the same” as the singularities of . As an application, we show that there are finitely many subschemes of a quasiprojective variety that are compatibly split by a given Frobenius splitting. We also reinterpret Fedder’s criterion in this context, which has some surprising implications.
Citation
Karl Schwede. "F-adjunction." Algebra Number Theory 3 (8) 907 - 950, 2009. https://doi.org/10.2140/ant.2009.3.907
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