Sudipta Das

Tata Institute of Fundamental Research, Mumbai

Generalized Hilbert-Kunz multiplicity for mfamilies of ideals

In this research, we initiate a systematic study of the generalized Hilbert–Kunz multiplicity for families of ideals in a Noetherian local ring $(R,\mathfrak{m})$ of positive characteristic, and introduce a new asymptotic invariant called the Amao-type multiplicity. We establish that, for a $p$-family of ideals, the generalized Hilbert–Kunz multiplicity arises as the limit of Amao-type multiplicities.