Characterizations of Regular Local Rings in Positive Characteristics

2007/02/18 by Jinjia Li, Li, Jinjia
Mathematics · #13A35 #13D07 #13D25 #13H05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A35 #msc:13D07 #msc:13D25 #msc:13H05

paper · pdf · doi:10.48550/arxiv.math/0702531

6 pages

openalex publication_date 2007/02/18 · arxiv created 2007/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ıt_i=\undersetn → ∞lim ł(\tor_i(k,^fn R))/p^nd. We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic p case. Our proof avoids using the existence of big Cohen-Macaulay modules, which is the major tool in the proof of Bridgeland and Iyengar.

Related

• Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension
• Regularity and finite injective dimension in characteristic p>0
• Lim Cohen-Macaulay sequences of modules
• The vanishing of Tor₁^R(R⁺,k) implies that R is regular
• Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular