Igusas P Adic Local Zeta Function And The Monodromy Conjecture For Non Degenerate Surface Singularities

Download Igusas P Adic Local Zeta Function And The Monodromy Conjecture For Non Degenerate Surface Singularities full books in PDF, epub, and Kindle. Read online free Igusas P Adic Local Zeta Function And The Monodromy Conjecture For Non Degenerate Surface Singularities ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities

Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities
Author :
Publisher : American Mathematical Soc.
Total Pages : 146
Release :
ISBN-10 : 9781470418410
ISBN-13 : 147041841X
Rating : 4/5 (41X Downloads)

Book Synopsis Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities by : Bart Bories

Download or read book Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities written by Bart Bories and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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∈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)⊂C3 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 B1-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.


Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities Related Books