93 citations · 220 across the 19 of their papers we have counts for
20 papers
Distribution modulo one of linear recurrent sequences
Zhangchi Chen, Zihao Ye, Weizhe Zheng
We study the distribution modulo one of linear recurrent sequences of real numbers. We prove criteria for the finiteness of the set of limit values of the fractional parts of such…
Alternating geometric progressions modulo one and Sturmian words
Qing Lu, Weizhe Zheng
Let be an integer. Using Sturmian words we describe all irrational real numbers such that the image in of the sequence is…
Fractional parts of powers of negative rationals
Qing Lu, Weizhe Zheng
We prove that for any real number and any coprime integers such that is irrational or , the image in of the sequence $(ξ(-p/q)^…
On a question of Astorg and Boc Thaler
Zhangchi Chen, Zihao Ye, Weizhe Zheng
Astorg and Boc Thaler studied the dynamics of certain skew-products tangent to the identity on , with two real parameters and derived from its coefficie…
Hodge-Riemann polynomials
Qing Lu, Weizhe Zheng
We show that Schur classes of ample vector bundles on smooth projective varieties satisfy Hodge-Riemann relations on under the assumption that vanishes. Mor…
Slopes and weights of -adic cohomology of rigid spaces
Qing Lu, Weizhe Zheng
We prove that Frobenius eigenvalues of -adic cohomology and -adic intersection cohomology of rigid spaces over -adic local fields are algebraic integers and we give…
On the distribution of multivariate Jacobi sums
Qing Lu, Weizhe Zheng
Let be a finite field of elements. We show that the normalized Jacobi sum ( nontrivial) is asymptotically equidistr…
Categorical traces and a relative Lefschetz-Verdier formula
Qing Lu, Weizhe Zheng
We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal -cat…
Compatible systems and ramification
Qing Lu, Weizhe Zheng
We show that compatible systems of -adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification.…
Duality and nearby cycles over general bases
Qing Lu, Weizhe Zheng
This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this commutation holds, confirming a pre…
Companions on Artin stacks
Weizhe Zheng
Deligne's conjecture that -adic sheaves on normal schemes over a finite field admit -companions was proved by L. Lafforgue in the case of curves and by Drinfeld in the…
Enhanced adic formalism and perverse t-structures for higher Artin stacks
Yifeng Liu, Weizhe Zheng
In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for étale cohomology of Artin stacks and prove several desired properties including the base cha…
Parity and symmetry in intersection and ordinary cohomology
Shenghao Sun, Weizhe Zheng
In this paper, we show that the Galois representations provided by -adic cohomology of proper smooth varieties, and more generally by -adic intersection cohomology of p…
On the distribution of Jacobi sums
Qing Lu, Weizhe Zheng, Zhiyong Zheng
Let be a finite field of elements. For multiplicative characters of , we let denote the Jacobi sum. Nic…
Quotient stacks and equivariant étale cohomology algebras: Quillen's theory revisited
Luc Illusie, Weizhe Zheng
Let be an algebraically closed field. Let be a noetherian commutative ring annihilated by an integer invertible in and let be a prime number different from the c…
Enhanced six operations and base change theorem for higher Artin stacks
Yifeng Liu, Weizhe Zheng
In this article, we develop a theory of Grothendieck's six operations for derived categories in étale cohomology of Artin stacks, for both torsion and adic coefficients. We prove s…
Gluing restricted nerves of -categories
Yifeng Liu, Weizhe Zheng
In this article, we develop a general technique for gluing subcategories of -categories. We obtain categorical equivalences between simplicial sets associated to certain mu…
Gluing pseudo functors via -fold categories
Weizhe Zheng
Gluing of two pseudo functors has been studied by Deligne, Ayoub, and others in the construction of extraordinary direct image functors in étale cohomology, stable homotopy, and mi…
Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks
Weizhe Zheng
Laszlo and Olsson constructed Grothendieck's six operations for constructible complexes on Artin stacks in étale cohomology under an assumption of finite cohomological dimension, w…
Odds and ends on finite group actions and traces
Luc Illusie, Weizhe Zheng
In this article, we study several problems related to virtual traces for finite group actions on schemes of finite type over an algebraically closed field. We also discuss applicat…