4 papers · 1 filter
Asymptotic vanishing conditions which force regularity in local rings of prime characteristic
Ian Aberbach, Jinjia Li
Let $(R,\m,k)$ be a local (Noetherian) ring of positive prime characteristic and dimension . Let $G_\dt$ be a minimal resolution of the residue field , and for each $i\ge…
Characterizations of Regular Local Rings in Positive Characteristics
Jinjia Li
In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher $\tor$ counterparts…
Characterizations of modules of finite projective dimension over complete intersections
Jinjia Li
Let be a finitely generated module over a local complete intersection of characteristic . The property that has finite projective dimension can be characterized by…
The Upper Bound of Frobenius Related Length Functions
Jinjia Li
In this paper, we study the asymptotic behavior of lengths of $\tor$ modules of homologies of complexes under the iterations of the Frobenius functor in positive characteristic. We…