6 papers · 1 filter
-Homotopy Types and Applications to Topology and Algebraic Geometry
Runjie Hu, Guozhen Wang
We develop a -homotopy theory for -complete spaces. To a -complete space , we associate a commutative differential graded algebra over by rect…
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…
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…
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…
Galois Symmetry of 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…
-theory Characteristic Classes
Runjie Hu
Although the local information of the -spectra is well understood, the problem of whether this local information can be identified with the geometric data for bundles remains op…