GENERALIZED HILBERT–KUNZ FUNCTION IN GRADED DIMENSION 2
Keyword(s):
We prove that the generalized Hilbert–Kunz function of a graded module $M$ over a two-dimensional standard graded normal $K$-domain over an algebraically closed field $K$ of prime characteristic $p$ has the form $gHK(M,q)=e_{gHK}(M)q^{2}+\unicode[STIX]{x1D6FE}(q)$, with rational generalized Hilbert–Kunz multiplicity $e_{gHK}(M)$ and a bounded function $\unicode[STIX]{x1D6FE}(q)$. Moreover, we prove that if $R$ is a $\mathbb{Z}$-algebra, the limit for $p\rightarrow +\infty$ of the generalized Hilbert–Kunz multiplicity $e_{gHK}^{R_{p}}(M_{p})$ over the fibers $R_{p}$ exists, and it is a rational number.
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2016 ◽
Vol 113
(19)
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pp. 5185-5188
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2018 ◽
Vol 71
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pp. 819-842
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1977 ◽
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pp. 237-252
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2019 ◽
Vol 18
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pp. 1950205
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1959 ◽
Vol 14
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pp. 223-234
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2013 ◽
Vol 89
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pp. 234-242
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2014 ◽
Vol 35
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pp. 2242-2268
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