Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities write by Bart Bories. This book was released on 2016-06-21. Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities available in PDF, EPUB and Kindle. 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.
$p$-Adic Analysis, Arithmetic and Singularities
$p$-Adic Analysis, Arithmetic and Singularities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook $p$-Adic Analysis, Arithmetic and Singularities write by Carlos Galindo. This book was released on 2022-05-11. $p$-Adic Analysis, Arithmetic and Singularities available in PDF, EPUB and Kindle. This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications. This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces $p$-adic analysis, the theory of Archimedean, $p$-adic, and motivic zeta functions, singularities of plane curves and their Poincaré series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists. This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.
Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems
Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems write by Igor Burban. This book was released on 2017-07-13. Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems available in PDF, EPUB and Kindle. In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups
Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups write by Matthew J. Emerton. This book was released on 2017-07-13. Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups available in PDF, EPUB and Kindle. The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.
On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps
On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps write by E. Delaygue. This book was released on 2017-02-20. On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps available in PDF, EPUB and Kindle. Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
