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- W2064876799 abstract "Let C be a characteristic p irreducible projective plane curve defined by a degree d form f, and n→en(f) be the Hilbert–Kunz function of f. en=μp2n−Rn with μ⩾3d4 and Rn=O(pn). When C is smooth, Rn=O(1); Brenner has shown the Rn to be eventually periodic when one further assumes C defined over a finite field. We generalize these results, dropping smoothness. An additional term, (periodic) pn now appears in Rn, with the periodic function taking values in 1d⋅Z[1p]. We describe it using 1-dimensional Hilbert–Kunz theory in the local rings of the singular points of C, together with sheaf theory on C, and work explicit examples." @default.
- W2064876799 created "2016-06-24" @default.
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- W2064876799 date "2007-10-01" @default.
- W2064876799 modified "2023-10-16" @default.
- W2064876799 title "Hilbert–Kunz functions for irreducible plane curves" @default.
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- W2064876799 doi "https://doi.org/10.1016/j.jalgebra.2007.03.028" @default.
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