Runjie Hu

activity

20232026

collaborators

9 papers

math.NT2026

Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces

Ruida Di, Runjie Hu

Let $E$ be an $n$ -dimensional rigid adelic space over a number field $K$ . We study the minimum number $g_{E} (R)$ of proper $K$ -subspaces needed to cover the projective height ball of…

math.AT2026

$Q_{p}$ -Homotopy Types and Applications to Topology and Algebraic Geometry

Runjie Hu, Guozhen Wang

We develop a $Q_{p}$ -homotopy theory for $p$ -complete spaces. To a $p$ -complete space $X$ , we associate a commutative differential graded algebra over $Q_{p}$ by rect…

math.GR2026

Continuous Mal'cev Qp-Completion of Pro-p Groups

Runjie Hu, Guozhen Wang

We give three explicit constructions of the continuous Mal'cev Qp-completion of a topologically finitely generated pro-p group, using Tannakian formalism, Hopf algebras and p-adic…

math.AG2026

Non-liftable varieties via etale cohomology rings

Runjie Hu, Siqing Zhang

We construct a smooth projective variety in positive characteristic whose $Q_{ℓ}$ -coefficient etale cohomology ring is not the scalar extension of any graded $\mathbb{Q…

math.AT2025

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups

Ruida Di, Runjie Hu, Siqing Zhang

In this paper, we introduce a necessary condition for the existence of characteristic zero liftings of certain smooth, proper varieties in positive characteristic, using etale homo…

math.AT2025

Formal Manifold Structures on Positive Characteristic Varieties

Runjie Hu, Siqing Zhang

In his 1970 ICM report, Sullivan proposes the program of l-adic formalization of the concept of manifolds. In this program, he claims that smooth positive characteristic varieties…

math.AT2023

A homotopical consequence of branched covers

Runjie Hu

We prove that the profinite completion of a pseudomanifold is the Artin-Mazur's etale homotopy type construction on its branched covers, which was implicitly conjectured by Sulliva…

math.AT2023

Galois Symmetry of $G a l (Q / Q)$ on Topological Manifold Structures of Varieties

Runjie Hu

We propose a definition of the profinite normal structure set for the set of all manifolds in a fixed profinite homotopy type. Using this framework, we prove that the Galois action…

math.AT2023

$L$ -theory Characteristic Classes

Runjie Hu

Although the local information of the $L$ -spectra is well understood, the problem of whether this local information can be identified with the geometric data for bundles remains op…

Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces

Qp​-Homotopy Types and Applications to Topology and Algebraic Geometry

Continuous Mal'cev Qp-Completion of Pro-p Groups

Non-liftable varieties via etale cohomology rings

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups

Formal Manifold Structures on Positive Characteristic Varieties

A homotopical consequence of branched covers

Galois Symmetry of Gal(Q​/Q) on Topological Manifold Structures of Varieties

L-theory Characteristic Classes

$Q_{p}$ -Homotopy Types and Applications to Topology and Algebraic Geometry

Galois Symmetry of $G a l (Q / Q)$ on Topological Manifold Structures of Varieties

$L$ -theory Characteristic Classes