93 citations · 220 across the 19 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…