Igusaâe(tm)s (Record no. 127900)
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| 000 -LEADER | |
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| fixed length control field | 07853nam a22005413i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4901864 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131324.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470429447 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470418410 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4901864 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4901864 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)948030099 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA614.58 .B67 2016 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.94 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Bories, Bart. |
| 245 10 - TITLE STATEMENT | |
| Title | Igusaâe(tm)s |
| Name of part/section of a work | |
| -- | Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (146 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.242 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 0. Introduction -- 0.1. Igusa's zeta function and the Monodromy Conjecture -- 0.2. Statement of the main theorem -- 0.3. Preliminaries on Newton polyhedra -- 0.4. Theorems of Denef and Hoornaert -- 0.5. Expected order and contributing faces -- 0.6. ₁-facets and the structure of the proof of the main theorem -- 0.7. Overview of the paper -- Acknowledgments -- Chapter 1. On the Integral Points in a Three-Dimensional Fundamental Parallelepiped Spanned by Primitive Vectors -- 1.0. Introduction -- 1.1. A group structure on -- 1.2. Divisibility among the multiplicities , ₁, ₂, ₃ -- 1.3. On the ₁ points of ₁ -- 1.4. On the ₁-coordinates of the points of -- 1.5. More divisibility relations -- 1.6. Explicit description of the points of -- 1.7. Determination of the numbers ₁, ₂, ₃, , ', ₀ from the coordinates of ₁, ₂, ₃ -- Chapter 2. Case I: Exactly One Facet Contributes to ₀ and this Facet Is a ₁-Simplex -- 2.1. Figure and notations -- 2.2. Some relations between the variables -- 2.3. Igusa's local zeta function -- 2.4. The candidate pole ₀ and its residue -- 2.5. Terms contributing to ₁ -- 2.6. The numbers _{ } -- 2.7. The factors _{ }( ₀) -- 2.8. Multiplicities of the relevant simplicial cones -- 2.9. The sums Σ(⋅)( ₀) -- 2.10. A new formula for ₁ -- 2.11. Formulas for Σ_{ } and Σ_{ } -- 2.12. A formula for _{ }=\mult _{ } -- 2.13. Description of the points of _{ } -- 2.14. A formula for Σ_{ } -- 2.15. Proof of ₁'=0 -- Chapter 3. Case II: Exactly One Facet Contributes to ₀ and this Facet Is a Non-Compact ₁-Facet -- 3.1. Figure and notations -- 3.2. The candidate pole ₀ and the contributions to its residue -- 3.3. The factors _{ }( ₀), the sums Σ(⋅)( ₀) and a new formula for ₁ -- 3.4. Proof of ₁'=0. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Chapter 4. Case III: Exactly Two Facets of Γ_{ } Contribute to ₀, and These Two Facets Are Both ₁-Simplices with Respect to a Same Variable and Have an Edge in Common -- 4.1. Figure and notations -- 4.2. Some relations between the variables -- 4.3. Igusa's local zeta function -- 4.4. The candidate pole ₀ and its residues -- 4.5. Terms contributing to ₂ and ₁ -- 4.6. The numbers _{ } -- 4.7. The factors _{ }( ₀) and _{ }'( ₀) -- 4.8. Multiplicities of the relevant simplicial cones -- 4.9. The sums Σ(⋅)( ₀) and Σ(⋅)'( ₀) -- 4.10. Simplified formulas for ₂ and ₁ -- 4.11. Vector identities -- 4.12. Points of _{ }, _{ }, _{ }, ₂, ₁ and additional relations -- 4.13. Investigation of the Σ_{∙} and the Σ_{∙}', except for Σ₁', Σ₃ -- 4.14. Proof of ₂=0 and a new formula for ₁ -- 4.15. Study of Σ₁' -- 4.16. An easier formula for the residue ₁ -- 4.17. Investigation of Σ₃ -- 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 -- 5.2. The candidate pole ₀ and the contributions to its residues -- 5.3. Towards simplified formulas for ₂ and ₁ -- 5.4. Some vector identities and their consequences -- 5.5. Points of ₓ, _{ }, and ₃ -- 5.6. Formulas for Σₓ,Σₓ', and Σ₃ -- 5.7. Proof of ₂'= ₁'=0 -- Chapter 6. Case V: Exactly Two Facets of Γ_{ } Contribute to ₀ -- One of Them Is a Non-Compact ₁-Facet, the Other One a ₁-Simplex -- These Facets Are ₁ with Respect to a Same Variable and Have an Edge in Common -- 6.1. Figure and notations -- 6.2. Contributions to the candidate pole ₀ -- 6.3. Towards simplified formulas for ₂ and ₁ -- 6.4. Investigation of the sums Σ_{∙} and Σ_{∙}' -- 6.5. Proof of ₂'= ₁'=0. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Chapter 7. Case VI: At Least Three Facets of Γ_{ } Contribute to ₀ -- All of Them Are ₁-Facets (Compact or Not) with Respect to a Same Variable and They Are 'Connected to Each Other by Edges' -- Chapter 8. General Case: Several Groups of ₁-Facets Contribute to ₀ -- Every Group Is Separately Covered By One of the Previous Cases, and the Groups Have Pairwise at Most One Point in Common -- Chapter 9. The Main Theorem for a Non-Trivial Character of _{ }^{×} -- Chapter 10. The Main Theorem in the Motivic Setting -- 10.1. The local motivic zeta function and the motivic Monodromy Conjecture -- 10.2. A formula for the local motivic zeta function of a non-degenerate polynomial -- 10.3. A proof of the main theorem in the motivic setting -- References -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 f^{-1}(0)\subset\mathbf{C}^3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B_1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Singularities (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | p-adic fields. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | p-adic groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Functions, Zeta. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Monodromy groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Algebraic. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Veys, Willem. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Bories, Bart |
| Title | Igusaâe(tm)s |
| -- | |
| -- | Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2016 |
| International Standard Book Number | 9781470418410 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901864">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901864</a> |
| Public note | Click to View |
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