Skip to main content

Asymptotic behavior of socle under Frobenius iterations

Date:
-

Let (R,m) be a standard-graded local algebra over a field of positive characteristic p. Suppose I is a m-primary ideal of R. We study how the top socle degree and the socle length of R/J behave asymptotically, where J is a (varying) Frobenius power of I. We will also discuss their relations with Hilbert-Kunz multiplicity/function and asymptotic behaviors (with respect to Frobenius iteration) of some other homological invariants.