7 citations · 28 across the 18 of their papers we have counts for
19 papers · 1 filter
Poincaré duality for pro-étale -local systems
Shizhang Li, Wiesława Nizioł, Emanuel Reinecke +1
We prove finiteness and Poincaré duality for pro-étale -local systems on proper -adic rigid-analytic spaces in the framework of Banach--Colmez spaces and establish…
On de Rham--Witt Cohomology of Classifying Stacks
Shizhang Li, Yuan Yang
We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in term…
Automorphisms of Frobenius twisted de Rham cohomology
Shizhang Li, Shubhodip Mondal
In this short paper, we prove that the moduli of automorphisms of Frobenius twisted de Rham cohomology functor is given by . Our method is to use the notion of $\math…
Bounding crystalline torsion from étale torsion
Ofer Gabber, Shizhang Li
In this note, we prove that given a smooth proper family over a -adic ring of integers, one gets a control of its crystalline torsion in terms of its étale torsion, the cohomolo…
Relative Poincaré duality in nonarchimedean geometry
Shizhang Li, Emanuel Reinecke, Bogdan Zavyalov
We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In…
Frobenius height of prismatic cohomology with coefficients
Haoyang Guo, Shizhang Li
We study the behavior of Frobenius operators on smooth proper pushforwards of prismatic F-crystals. In particular we show that the i-th pushforward has its Frobenius height increas…
On the u^{\infty}-torsion submodule of prismatic cohomology
Shizhang Li, Tong Liu
We investigate the maximal finite length submodule of the Breuil-Kisin prismatic cohomology of a smooth proper formal scheme over a p-adic ring of integers. This submodule governs…
Exponentially twisted de Rham cohomology and rigid cohomology
Shizhang Li, Dingxin Zhang
We prove a comparison theorem between exponentially twisted de Rham cohomology and rigid cohomology with coefficients in a Dwork crystal.
On endomorphisms of the de Rham cohomology functor
Shizhang Li, Shubhodip Mondal
We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applicati…
Totaro's inequality for classifying spaces
Bhargav Bhatt, Shizhang Li
For a complex Lie group G and a prime number p, Totaro had conjectured that the dimension of the singular cohomology with Z/p-coefficients of classifying space of G is bounded abov…
Comparison of prismatic cohomology and derived de Rham cohomology
Shizhang Li, Tong Liu
We establish a comparison isomorphism between prismatic cohomology and derived de Rham cohomology respecting various structures, such as their Frobenius actions and filtrations. As…
Period sheaves via derived de Rham cohomology
Haoyang Guo, Shizhang Li
In this article we give an interpretation, in terms of derived de Rham complexes, of Scholze's de Rham period sheaf and Tan--Tong's crystalline period sheaf.
Integral p-adic Hodge filtrations in low dimension and ramification
Shizhang Li
Given an integral p-adic variety, we observe that if the integral Hodge--de Rham spectral sequence behaves nicely, then the special fiber knows the Hodge numbers of the generic fib…
An example of liftings with different Hodge numbers
Shizhang Li
In this paper, we exhibit an example of a smooth proper variety in positive characteristic possessing two liftings with different Hodge numbers.
Logarithmic de Rham comparison for open rigid spaces
Shizhang Li, Xuanyu Pan
In this note, we prove the logarithmic -adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal cros…
Line bundles on rigid varieties and Hodge symmetry
David Hansen, Shizhang Li
We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theore…
Semistable reduction for multi-filtered vector spaces
Shizhang Li
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
On rigid varieties with projective reduction
Shizhang Li
In this paper, we study smooth proper rigid varieties which admit formal models whose special fibers are projective. The main theorem asserts that the identity components of the as…
Unobstructedness of deformations of Calabi-Yau varieties with a line bundle
Shizhang Li, Xuanyu Pan
We generalize the Tian-Todorov Theorem in the case of Calabi-Yau varieties equipped with a line bundle.