Related papers: A relative Segre zeta function

We construct two families of refinements of the (projectivized) support variety of a finite dimensional module $M$ for a finite group scheme $G$. For an arbitrary finite group scheme, we associate a family of {\it non maximal rank…

Let $p$ and $l$ be rational primes such that $l$ is odd and the order of $p$ modulo $l$ is even. For such primes $p$ and $l$, and for $e=l, 2l$, we consider the non-singular projective curves $aY^e = bX^e + cZ^e$ ($abc \neq 0$) defined over…

Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain 'motivic integral', living in a completion of the Grothendieck ring of algebraic varieties. He used this…

In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary k poles of prescribed orders, such that for every geometric point f in…

We introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series. We prove the meromorphic continuation of this zeta function and identify its poles and their residues.…

We prove 2-out-of-3 property for rationality of motivic zeta function in distinguished triangles in Voevodsky's category DM. As an application, we show rationality of motivic zeta functions for all varieties whose motives are in the thick…

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

This paper studies zeta functions of the form $\sum_{n=1}^{\infty} \chi(n) n^{-s}$, with $\chi$ a completely multiplicative function taking only unimodular values. We denote by $\sigma(\chi)$ the infimum of those $\alpha$ such that the…

Let S be a smooth projective surface equipped with a line bundle H. Lehn's conjecture is a formula for the top Segre class of the tautological bundle associated to H on the Hilbert scheme of points of S. Voisin has recently reduced Lehn's…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…

Given a hypersurface, $X$, prime $p$, the zeta function is a generating function for the number of $\mathbb{F}_{p}$ rational points of $X$. Until now, there is no algorithm for computing hypersurfaces with ADE singularities. Scott Stetson…

Let $G$ be a profinite group. A strongly admissible smooth representation $\rho$ of $G$ over $\mathbb{C}$ decomposes as a direct sum $\rho \cong \bigoplus_{\pi \in \mathrm{Irr}(G)} m_\pi(\rho) \, \pi$ of irreducible representations with…

For a smooth family F of admissible elliptic pseudodifferential operators with differential form coefficients associated to a geometric fibration of manifolds M--> B we show that there is a natural zeta-form z(F,s) and zeta-determinant-…

For any ring $R$, we introduce an invariant in the form of a partially ordered abelian semigroup $\mathrm{S}(R)$ built from an equivalence relation on the class of countably generated projective modules. We call $\mathrm{S}(R)$ the Cuntz…

We introduce the concise secant varieties, which are, informally speaking, modular partial desingularisations of secant varieties to Segre embeddings. More precisely, they are projective and birational to the abstract secant varieties, yet…

Let E and F be vector bundles over a complex projective smooth curve X, and suppose that 0 -> E -> W -> F -> 0 is a nontrivial extension. Let G be a subbundle of F, and D an effective divisor on X. We give a criterion for the subsheaf G(-D)…

In this paper, we investigate Weng zeta functions associated with curves of genus 2 over finite fields. Building upon Weng's framework for non-abelian zeta functions, we establish that, as the rank n tends to infinity, the Riemann…

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser…

Stillman posed a question as to whether the projective dimension of a homogeneous ideal I in a polynomial ring over a field can be bounded by some formula depending only on the number and degrees of the minimal generators of I. More…