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Author Bories, Bart, 1980- author.

Title Igusa's p-adic local zeta function and the Monodromy conjecture for non-degenerate surface singularities / Bart Bories, Willem Veys
Published Providence, Rhode Island : American Mathematical Society, 2016
©2016
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Description 1 online resource (vii, 131 pages) : illustrations
Series Memoirs of the American Mathematical Society, 0065-9266 ; volume 242, number 1145
Memoirs of the American Mathematical Society ; no. 1145
Contents 880-01 Introduction -- On the Integral Points in a Three-Dimensional Fundamental Parallelepiped Spanned by Primitive Vectors -- Case I: Exactly One Facet Contributes to s₀ and this Facet Is a B₁-Simplex -- Case II: Exactly One Facet Contributes to s₀ and this Facet Is a Non-Compact B₁-Facet -- Case III: Exactly Two Facets of [Gamma][subcript f] Contribute to s₀, and These Two Facets Are Both B₁-Simplices with Respect to a Same Variable and Have an Edge in Common -- Case IV: Exactly Two Facets of [Gamma][subscript f] Contribute to s₀, and These Two Facets Are Both Non-Compact B₁-Facets with Respect to a Same Variable and Have an Edge in Common -- Case V: Exactly Two Facets of [Gamma][subscript f] Contribute to s₀; One of Them Is a Non-Compact B₁-Facet, the Other One a B₁-Simplex; These Facets Are B₁ with Respect to a Same Variable and Have an Edge in Common -- Case VI: At Least Three Facets of [Gamma][subscript f] Contribute to s₀; All of Them Are B₁-Facets (Compact or Not) with Respect to a Same Variable and They Are 'Connected to Each Other by Edges' -- General Case: Several Groups of B₁-Facets Contribute to s₀; Every Group Is Separately Covered By One of the Previous Cases, and the Groups Have Pairwise at Most One Point in Common -- The Main Theorem for a Non-Trivial c Character of Z[subscript p][suberscript x] -- The Main Theorem in the Motivic Setting
880-01 4.12. Points of _{ }, _{ }, _{ }, ₂, ₁ and additional relations4.13. Investigation of the Σ_{∙} and the Σ_{∙}', except for Σ(B', Σ(B; 4.14. Proof of ₂=0 and a new formula for ₁; 4.15. Study of Σ(B'; 4.16. An easier formula for the residue ₁; 4.17. Investigation of Σ(B; 4.18. Proof that the residue ₁ equals zero; Chapter 5. Case IV: Exactly Two Facets of Γ_{ } Contribute to ₀, and These Two Facets Are Both Non-Compact ₁-Facets with Respect to a Same Variable and Have an Edge in Common; 5.1. Figure and notations
Summary In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f\in\mathbf{Z}[x, y, z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f̂{-1}(0)\subset\mathbf{C}̂3 close to the origin. Essentially the
Notes "Volume 242, number 1145 (second of 4 numbers), July 2016."
Bibliography Includes bibliographical references (pages 129-131)
Notes Online resource; title from PDF title page (viewed April 27, 2016)
Subject Functions, Zeta.
Geometry, Algebraic.
Monodromy groups.
Singularities (Mathematics)
p-adic fields.
p-adic groups.
Functions, Zeta.
Geometry, Algebraic.
Monodromy groups.
Singularities (Mathematics)
p-adic fields.
p-adic groups.
Form Electronic book
Author Veys, Wim, 1963- author.
American Mathematical Society, publisher.
ISBN 1470429446
9781470429447