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Notes on the Hilbert–Kunz function

✍ Scribed by Douglas Hanes

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
113 KB
Volume
265
Category
Article
ISSN
0021-8693

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✦ Synopsis

We note certain properties of the Hilbert-Kunz function and Hilbert-Kunz multiplicity, including a strengthened inequality between Hilbert-Kunz and Hilbert-Samuel multiplicities and a characterization of a mixed Hilbert function incorporating both ordinary and Frobenius powers of ideals.

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We determine the Hilbert᎐Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert᎐Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of Hilbert᎐Kunz functions of plane cubics. C