Related papers: Characteristic Epsilon Cycles of $\ell$-adic Sheav…

We introduce a notion of compatibility for families $(\mathcal{F}_{\ell})_{\ell}$ of bounded constructible $\ell$-adic complexes of \'etale sheaves on schemes. For schemes of finite type over a field, this notion is preserved by the usual…

We define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula a la Milnor for the total…

Let $S$ be a noetherian scheme and $f\colon X\to S$ be a smooth morphism of relative dimension 1. For a locally constant sheaf on the complement of a divisor in $X$ at over $S$, Deligne and Laumon proved that the universal local acyclicity…

We study some properties of the characteristic cycle of a constructible complex on a smooth variety over a perfect field, push-forward and product.

Given an abelian variety $A$ defined over a finite field $k$, we say that $A$ is "cyclic" if its group $A(k)$ of rational points is cyclic. In this paper we give a bijection between cyclic abelian varieties of an ordinary isogeny class…

We define the singular support of an $\ell$-adic sheaf on a smooth variety over any field. To do this, we combine Beilinson's construction of the singular support for torsion \'etale sheaves with Hansen and Scholze's theory of universal…

Let $f\colon X\to\mathbb{A}^1_k$ be a morphism from a smooth variety to an affine line with an isolated singular point. For such a singularity, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other…

Let $X$ be a smooth scheme over a finite field of characteristic $p$. In answer to a conjecture of Deligne, we establish that for any prime $\ell \neq p$, an $\ell$-adic Weil sheaf on $X$ which is algebraic (or irreducible with finite…

Brylinski and Malgrange proved in 1986 that, for a monodromic algebraic D-module on a finite dimensional vector space over the complex numbers, its characteristic cycle is canonically identified with the characteristic cycle of its Fourier…

For a prime number $\ell$, an isogeny class $\mathcal{A}$ of abelian varieties is called $\ell$-cyclic if every variety in $\mathcal{A}$ have a cyclic $\ell$-part of its group of rational points. More generally, for a finite set of prime…

Let $\cal A$ be a maximal (or more generally a hereditary) order in a central simple algebra over a global field $F$ of positive characteristic. We study the reduction of the modular scheme of $\cal A$-elliptic sheaves at all places of $F$.…

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…

We prove a number of results on the \'etale cohomology of rigid analytic varieties over $p$-adic non-archimedean local fields. Among other things, we establish bounds for Frobenius eigenvalues, show a strong version of Grothendieck's local…

Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…

We prove a twist formula for the epsilon factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula is a modified version of the formula conjectured by Kato…

Relying on the formalism developed by Alexander Beilinson and Takeshi Saito, we compute the characteristic cycle of an external symmetric power of a tame \'etale sheaf on a curve. This generalizes a result of G\'erard Laumon in…

For a smooth morphism $f: X \longrightarrow \Sigma$ of real analytic manifolds and an $\mathbb{R}$-constructible sheaf $F$ on $X$ satisfying some condition, we define a family of Lagrangian cycles parameterized by $\Sigma$ that we call the…

Recently, the singular support and the characteristic cycle of an \'etale sheaf on a smooth variety over a perfect field are constructed by Beilinson and Saito, respectively. In this article, we extend the singular support to a relative…

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

We show that the characteristic cycle of the exterior product of constructible complexes is the exterior product of the characteristic cycles of factors. This implies the compatibility of characteristic cycles with smooth pull-back which is…