Related papers: Global Igusa zeta function and $K$-equivalence

Goss zeta values can be found, in some cases, as evaluations of a new type of rigid analytic function on projective curves $X$ over a finite field $\mathbb{F}_q$, called "Pellarin $L$-series". In the case of genus $0$ and $1$, Pellarin and…

Following an idea of Ishida, we develop polynomial equations for certain unramified double covers of surfaces with p_g=q=1 and K^2=2. Our first main result provides an explicit surface surface X with these invariants defined over Q that has…

Let $X$ be a perfectoid space with tilt $X^\flat$. We construct a canonical map $\theta:\operatorname{Pic} X^\flat\to\lim\operatorname{Pic} X$ where the (inverse) limit is taken over the $p$-power map, and show that $\theta$ is an…

Let A be the coordinate ring of an affine elliptic curve (over an infinite field k) of the form X-{p}, where X is projective and p is a closed point on X. Denote by F the function field of X. We show that the image of H_*(GL_2(A),Z) in…

Let $Gr(k,n)$ be the Pl\"ucker embedding of the Grassmann variety of projective $k$-planes in $\P n$. For a projective variety $X$, let $\sigma_s(X)$ denote the variety of its $s-1$ secant planes. More precisely, $\sigma_s(X)$ denotes the…

Let K be a field of characteristic 0 and A be a rigid tensor K-linear category. Let M be a finite-dimensional object of A in the sense of Kimura-O'Sullivan. We prove that the "motivic" zeta function of M with coefficients in K\_0(A) has a…

Throughout this paper, k is a number field. We fix a quadratic extension k_1=k(a_0) of k, where a_0=sqrt(B_0) for a certain B_0 in k^\times/(k^\times)^2. In this paper, we consider the zeta function defined for the space of pairs of binary…

Let $k$ be a function field of one variable over a finite field with the characteristic not equal to two. In this paper, we consider the prehomogeneous representation of the space of binary quadratic forms over $k$. We have two main…

This paper provides specific results on the Igusa local zeta function for the curves $x^n+y^m$. In addition to specific results, we give an introduction to $p$-adic analysis and a discussion of various methods which have been used to…

Let $(M,g)$ be a smooth Riemannian manifold, $K$ a compact Lie group and $p:P\to M$ a principal $K$-bundle over $M$ endowed with a connection $A$. Fixing a bi invariant inner product on Lie algebra $\mathfrak{k}$ of $K$, the connection $A$…

Let $k$ be a field, $f \colon X \to Y$ a birational morphism of integral connected schemes proper over $k$ with $Y$ normal, $x \in X(k)$ lying over $y \in Y(k)$. For Tannakian categories $\cC_X \subset \Vect(X)$ and $\cC_Y \subset…

If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading…

Let $K$ be a complete discrete valued field with residue field $k$ and $F$ the function field of a curve over $K$. Let $A \in {}_2Br(F)$ be a central simple algebra with an involution $\sigma$ of any kind and $F_0 =F^{\sigma}$. Let $h$ be…

In this article, we study the zeros of the partial sums of the Dedekind zeta function of a cyclotomic field $K$ defined by the truncated Dirichlet series \[ \zeta_{K, X} (s) = \sum_{\|\mathfrak{a}\| \leq X} \frac{1}{\|\mathfrak{a}\|^{s}},…

Let $X$ be an $n$-dimensional normal $\mathbb{Q}$-factorial projective variety with canonical singularities and Picard number one such that $X$ is smooth in codimension two, $-K_X$ is ample and $n\geq 2$. We prove that $X$ satisfies the…

We prove an analogue of Fujino and Mori's ``bounding the denominators'' in the log canonical bundle formula (see also Prokhorov and Shokurov) for Kawamata log terminal pairs of relative dimension one. As an application we prove that for a…

Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic generic fiber $X$. We obtain a global equivalence between the category $\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational Hodge--Tate crystals…

Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$…

We study CAT(kappa) spaces X admitting affine functions. We show that there exists a canonical isometric embedding X -> Y x H where H is a Hilbert space, such that every affine function f: X -> R factors as f'o p, where p is the projection…

We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main…