2025/01/28 by Rodríguez-Villalobos, Sandra, Schwede, Karl
#13A35 #13B22 #13C14 #14B05 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.16773
Generalizing previous work of the first author, we introduce and study a characteristic free analog of the F-threshold for non-principal ideals. We show that this coincides with the classical F-threshold for weakly F-regular rings and that the set of F-thresholds coincides with the set of F-jumping numbers in a regular ring. We obtain results on F-thresholds of parameter ideals analogous to results of Huneke-Mustaţă-Takagi-Watanabe. Instead of taking ordinary powers of ideal, our definition uses fractional integral closure in an absolute integral closure of our ambient ring.