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- W2950492784 abstract "In this paper, we investigate the lower bound s HK ( p, d ) of Hilbert-Kunz multiplicities for non-regular unmixed local rings of Krull dimension d containing a field of characteristic p > 0. Especially, we focus on three-dimensional local rings. In fact, as a main result, we will prove that s HK ( p , 3) = 4/3 and that a three-dimensional complete local ring of Hilbert-Kunz multiplicity 4/3 is isomorphic to the non-degenerate quadric hypersurface k[[X, Y, Z,W ]]/( X 2 + Y 2 + Z 2 + W 2 ) under mild conditions. Furthermore, we pose a generalization of the main theorem to the case of dim A ≥ 4 as a conjecture, and show that it is also true in case dim A = 4 using the similar method as in the proof of the main theorem." @default.
- W2950492784 created "2019-06-27" @default.
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- W2950492784 date "2005-01-01" @default.
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- W2950492784 title "Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings" @default.
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- W2950492784 doi "https://doi.org/10.1017/s0027763000009053" @default.
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