相关论文: Weil-etale cohomology and special values of L-func…

We construct the Weil-\'etale cohomology and Euler characteristics for a subclass of the class of $\mathbb{Z}$-constructible sheaves on an open subscheme of the spectrum of the ring of integers of a number field. Then we show that the…

We construct a well-behaved Weil-\'etale complex for a large class of $\mathbb{Z}$-constructible sheaves on a regular irreducible scheme $U$ of finite type over $\mathbb{Z}$ and of dimension $1$. We then give a formula for the special value…

We define a Weil-\'etale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex $\mathbb{Z}^c$) of a large class of $\mathbb{Z}$-constructible sheaves on an integral $1$-dimensional proper arithmetic…

Let $X$ be a variety over a finite field. Given an order $R$ in a semi-simple algebra over the rationals and a constructible \'etale sheaf $F$ of $R$-modules over $X$, one can consider a natural non-commutative $L$-function associated with…

We would like to construct a new Grothendieck topology for arithmetic schemes, whose cohomology groups associated with motivic complexes of sheaves are finitely generated and whose Euler characteristics are related to special values of…

Lichtenbaum has conjectured the existence of a Grothendieck topology for an arithmetic scheme $X$ such that the Euler characteristic of the cohomology groups of the constant sheaf $\mathbb{Z}$ with compact support at infinity gives, up to…

Following the ideas of Flach and Morin (Doc. Math. 23 (2018), 1425--1560), we state a conjecture in terms of Weil-\'etale cohomology for the vanishing order and special value of the zeta function $\zeta (X, s)$ at $s = n < 0$, where $X$ is…

For a prime number p and a number field k, we first study certain etale cohomology groups with coefficients associated to a p-adic Artin representation of its Galois group, where we twist the coefficients using a modified Tate twist with a…

A lot of good properties of etale cohomology only hold for torsion coefficients. We use "enlargement of categories" as developed in http://arxiv.org/abs/math.CT/0408177 to define a cohomology theory that inherits the important properties of…

We give a direct description of the category of sheaves on Lichtenbaum's Weil-\'etale site of a number ring. Then we apply this result to define a spectral sequence relating Weil-\'etale cohomology to Artin-Verdier \'etale cohomology.…

Let $X$ be an arithmetic scheme (i.e., separated, of finite type over $\operatorname{Spec} \mathbb{Z}$) of Krull dimension $1$. For the associated zeta function $\zeta (X,s)$, we write down a formula for the special value at $s = n < 0$ in…

We combine work of Cox on the total coordinate ring of a toric variety and results of Eisenbud-Mustata-Stillman and Mustata on cohomology of toric and monomial ideals to obtain a formula for computing the Euler characteristic of a Weil…

We define and study a Weil-\'etale topos for any regular, proper scheme $X$ over $\Spec(Z)$ which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with $R$-coefficients has the expected…

We calculate the total derived functor for the map from the Weil-etale site introduced by Lichtenbaum to the etale site for varieties over finite fields. In particular, there is a long exact sequence relating Weil-etale cohomology and etale…

Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560) Weil-\'etale cohomology $H^i_\text{W,c} (X, \mathbb{Z} (n))$ for a proper, regular arithmetic scheme $X$ (i.e. separated and of finite type over $\operatorname{Spec}…

We introduce an exact category of torsion-free constructible tori and an abelian category of constructible tori over a Dedekind scheme with perfect residue fields. The first one has an explicit description as $2$-term complexes of smooth…

We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for separated schemes of finite type over a finite field, which should play a role analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective…

The purpose of this paper is to give a formula for the leading coefficient at $s=1$ of the $L$-function of one-motives over function fields in terms of Weil-\'etale cohomology, generalizing the Weil-\'etale version of the Birch and…

Lichtenbaum conjectured the existence of a Weil-\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme $\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\'e…

We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is…