26 citations · 67 across the 16 of their papers we have counts for
16 papers
-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…
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…
On the Last Kervaire Invariant Problem
Weinan Lin, Guozhen Wang, Zhouli Xu
We prove that the element is a permanent cycle in the Adams spectral sequence. As a result, we establish the existence of smooth framed manifolds with Kervaire invariant on…
Machine Proofs for Adams Differentials and Extension Problems among CW Spectra
Weinan Lin, Guozhen Wang, Zhouli Xu
In this document, we describe the process of obtaining numerous Adams differentials and extensions using computational methods, as well as how to interpret the dataset uploaded to…
-graded homotopy fixed point spectral sequence for height Morava -theory
Zhipeng Duan, Hana Jia Kong, Guchuan Li +2
We consider and as finite subgroups of the Morava stabilizer group which acts on the height Morava -theory at the prime .…
Topological Cyclic Homology of Local Fields
Ruochuan Liu, Guozhen Wang
We introduce a new approach to determining the structure of topological cyclic homology by means of a descent spectral sequence. We carry out the computation for a p-adic local fie…
The Chow -structure on the -category of motivic spectra
Tom Bachmann, Hana Jia Kong, Guozhen Wang +1
We define the Chow -structure on the -category of motivic spectra over an arbitrary base field . We identify the heart of this -structure $SH(k)^{c\heartsu…
Stable homotopy groups of spheres
Daniel C. Isaksen, Guozhen Wang, Zhouli Xu
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new computational method that yields a streamlined computation of the first 61 stable…
Stable homotopy groups of spheres: From dimension 0 to 90
Daniel C. Isaksen, Guozhen Wang, Zhouli Xu
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for …
The slice spectral sequence of a -equivariant height-4 Lubin-Tate theory
Michael A. Hill, XiaoLin Danny Shi, Guozhen Wang +1
We completely compute the slice spectral sequence of the -spectrum . After periodization and -localization, this spectrum is equivalent to…
The special fiber of the motivic deformation of the stable homotopy category is algebraic
Bogdan Gheorghe, Guozhen Wang, Zhouli Xu
For each prime , we define a -structure on the category of harmonic -motivic left module spectra over $\widehat…
Hurewicz Images of Real Bordism Theory and Real Johnson-Wilson Theories
Guchuan Li, XiaoLin Danny Shi, Guozhen Wang +1
We show that the Hopf elements, the Kervaire classes, and the -family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to t…
Some extensions in the Adams spectral sequence and the 51-stem
Guozhen Wang, Zhouli Xu
We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of is $\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus…
The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra
Guozhen Wang, Zhouli Xu
In this note, we use Curtis's algorithm and the Lambda algebra to compute the algebraic Atiyah-Hirzebruch spectral sequence of the suspension spectrum of with…
The triviality of the 61-stem in the stable homotopy groups of spheres
Guozhen Wang, Zhouli Xu
We prove that the 2-primary is zero. As a consequence, the Kervaire invariant element is contained in the strictly defined 4-fold Toda bracket $\langle 2, θ_4, θ_4,…
The monochromatic Hopf invariant
Guozhen Wang
In this paper we will compute the effect of the James-Hopf map after applying the Bousfield-Kuhn functor on Morava E-theory, and then compute the monochromatic Hopf invariant of th…