REFERENCES
- Aoyama , Y. ( 1983 ). Some basic results on canonical modules . J. Math. Kyoto Univ. 23 : 85 – 94 .
- Bruns , W. , Herzog , J. ( 1993 ). Cohen-Macaulay Rings . Cambridge Studies in Advanced Mathematics , Vol. 39 . Cambridge University Press .
- Chan , C.-Y. J. ( 1999 ). Filtrations of modules, the Chow group and the Grothendieck group . J. Algebra 219 : 330 – 344 .
- Fulton , W. ( 1998 ). Intersection Theory. , 2nd ed. Berlin : Springer .
- Han , C. , Monsky , P. ( 1993 ). Some surprising Hilbert–Kunz functions . Math. Z. 214 : 119 – 135 .
- Herzog , J. , et al. . ( 1971 ). Der kanonische Modul eines Cohen-Macaulay-Rings . Lect. Notes Math. , Vol. 238 . Springer-Verlag .
- Hochster , M. , Huneke , C. ( 1993 ). Phantom homology . Mem. Amer. Math. Soc. 103 .
- Hochster , M. , Yao , Y. Second coefficients of Hilbert-Kunz functions for domains. Preliminary preprint available at http://www.math.lsa.umich.edu/~hochster/hk.pdf .
- Huneke , C. , McDermott , M. , Monsky , P. ( 2004 ). Hilbert-Kunz functions for normal rings . Math. Res. Letters 11 : 539 – 546 .
- Kamoi , Y. , Kurano , K. ( 2002 ). On maps of Grothendieck groups induced by completion . J. Algebra 254 : 21 – 43 .
- Kunz , E. ( 1969 ). Characterizations of regular local rings for characteristic p . Amer. J. Math. 91 : 772 – 784 .
- Kurano , K. ( 2004 ). Numerical equivalence defined on Chow groups of Noetherian local rings . Invent. Math. 157 : 575 – 619 .
- Kurano , K. (2006). The singular Riemann-Roch theorem and Hilbert-Kunz functions. J. Algebra 304:487–499.
- Miller , C. ( 2000 ). A Frobenius characterization of finite projective dimension over complete intersections . Math. Z. 233 ( 1 ): 127 – 136 .
- Matsumura , H. ( 1994 ). Commutative Ring Theory . New York : Cambridge University Press .
- Monsky , P. ( 1983 ). The Hilbert-Kunz function . Math. Ann. 263 : 43 – 49 .
- Nagata , M. ( 1962 ). Local Rings . New York : Interscience Publishers .
- Roberts , P. ( 1987 ). Le théorème d'intersection . C. R. Acad. Sci. Paris Sér. I Math. 304 : 177 – 180 .
- Roberts , P. ( 1998 ). Multiplicities and Chern Classes in Local Algebra . Cambridge Tracts in Mathematics , Vol. 133 . Cambridge University Press .
- Roberts , P. , Srinivas , V. ( 2003 ). Modules of finite length and finite projective dimension . Invent. Math. 151 : 1 – 27 .
- Seibert , G. ( 1989 ). Complexes with homology of finite length and Frobenius functors . J. Algebra 125 : 278 – 287 .
- Srinivas , V. ( 1996 ). Algebraic K-Theory. , 2nd ed. Progress in Mathematics . Boston : Birkhauser .
- Swanson , I. , Huneke , C. ( 2006 ). Integral Closure of Ideals, Rings, and Modules . Lecture Notes Series , Vol. 336 . London Mathematical Society , Cambridge : Cambridge University Press .
- Communicated by U. Walther.