Abstract
Abstract
We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes F-nilpotent curves. Further, we show that a reduced, local F-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities of Frobenius test exponents along purely inseparable ring extensions with applications to F-nilpotent affine semigroup rings.
Publisher
Cambridge University Press (CUP)
Reference26 articles.
1. Uniform behaviour of the Frobenius closures of ideals generated by regular sequences
2. A connectedness result in positive characteristic
3. F-rational rings have rational singularities
4. $F$
-nilpotent rings and permanence properties;Kenkel;J. Comm. Algebra,2023
5. [13] Maddox, K. and Miller, L. E. , Generalized F-depth and graded nilpotent singularities, preprint, arXiv:2101.00365, 2021.