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Meuser, D.

On the poles of a local zeta function for curves. (English) Zbl 0503.14009

Invent. Math. 73, 445-465 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0503.14009

Cited in 2 Reviews
Cited in 12 Documents

MSC:

14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H25 Arithmetic ground fields for curves
14G20 Local ground fields in algebraic geometry
14H20 Singularities of curves, local rings
14E15 Global theory and resolution of singularities (algebro-geometric aspects)

Keywords:

simplicity of poles of zeta function; nonarchimedean ground field; curve with isolated singularity; desingularization
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Full Text: DOI EuDML

References:

[1] Bernstein, I.N., Gel’fand, S.I.: Meromorphic property of the functionP ?. Functional Anal. Appl.3, 68-69 (1969) · Zbl 0208.15201 · doi:10.1007/BF01078276
[2] Hironaka, H.: Introduction to the Theory of Infinitely Near Singular Points, Memorias de Matematica del Istituto ?Jorge Juan?, 28,Madrid, 1974 · Zbl 0366.32007
[3] Igusa, J.-I.: On the first terms of certain asymptotic expansions. Complex analysis and algebraic geometry. (Baily, W.L., Jr., Shioda, T., eds.) Cambridge University Press, 1977, pp. 357-368
[4] Igusa, J.-I.: Some observations in higher degree characters. Am. J. Math.99, 393-417 (1977) · Zbl 0373.12008 · doi:10.2307/2373827
[5] Strauss, L.: On the evaluation of certain integrals through desingularization. Ph.D. thesis; Johns Hopkins University, 1978
[6] Zariski, O.: Algebraic Surfaces. Ergeb. der Math., Springer (1932); Chelsea (1948) · JFM 61.0704.01
[7] Zariski, O.: Studies in equisingularity III, Saturation of local rings and equisingularity. Amer. J. Math.90, 961-1023 (1968) · Zbl 0189.21405 · doi:10.2307/2373492
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