Characterizations of Regular Local Rings in Positive Characteristics

الأصل · EN

In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher counterparts ıtᵢ=n → ∞ ł(ᵢ(k,ᶠⁿ R))/pnd. 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.