4 citations · 5 across the 15 of their papers we have counts for
15 papers
-Categorical Perverse -adic Differential Equations over Stacks
Xin Tong
We will discuss -categorical perverse -adic differential equations over stacks. On one hand, we are going to study some -adic analogous results of the Drinfeld's orig…
Geometric and Representation Theoretic Aspects of -adic Motives
Xin Tong
In this dissertation, we discuss mainly the corresponding geometric and representation theoretic aspects of relative -adic Hodge theory and -adic motives. To be more precise,…
Topologization and Functional Analytification II: -Categorical Motivic Constructions for Homotopical Contexts
Xin Tong
This is our second scope of the consideration on the corresponding topologization and the corresponding functional analytification. We will focus on the corresponding functorial an…
-Categorical Approaches to Hodge-Iwasawa Theory I: Introduction and Extensions
Xin Tong
In this paper, we give the introduction to the Hodge-Iwasawa Theory introduced by the author. After that we will give some well-defined extensions to the already shaped framework e…
-Categorical Functional Analysis and -adic Motives
Xin Tong
We discuss the deep relationship between -categorical functional analysis and the anticipated theory of -adic motives. The motivation fundamentally comes from applicatio…
Period Rings with Big Coefficients and Applications III
Xin Tong
We continue our study on the corresponding period rings with big coefficients, with the corresponding application in mind on relative -adic Hodge theory and noncommutative analy…
Topics on Geometric and Representation Theoretic Aspects of Period Rings I
Xin Tong
We consider more general framework than the corresponding one considered in our previous work on the Hodge-Iwasawa theory. In our current consideration we consider the correspondin…
Topologization and Functional Analytification I: Intrinsic Morphisms of Commutative Algebras
Xin Tong
Eventually after Dieudonné-Grothendieck, we give intrinsic definitions of étale, lisse and non-ramifié morphisms for general adic rings and general locally convex rings. And we inv…
Period Rings with Big Coefficients and Application II
Xin Tong
We continue our study on the corresponding noncommutative deformation of the relative -adic Hodge structures of Kedlaya-Liu along our previous work. In this paper, we are going…
Analytic Geometry and Hodge-Frobenius Structure Continued
Xin Tong
This is our sequel to our previous work on the corresponding generalized Frobenius modules over some big multivariate Robba rings. We will go beyond our previous discussion where w…
Period Rings with Big Coefficients and Applications I
Xin Tong
Following ideas of Kedlaya-Liu, we are going to consider extending our previous work to the context of more general adic spaces, which will be corresponding deformation of the rela…
Category and Cohomology of Hodge-Iwasawa Modules
Xin Tong
In this paper we study the corresponding categories and the corresponding cohomologies of the Hodge-Iwasawa modules we developed in our series papers on Hodge-Iwasawa theory. The c…
Analytic Geometry and Hodge-Frobenius Structure
Xin Tong
In this paper, we study Frobenius structures in higher dimensional -adic analytic geometry and the corresponding -adic functional analysis. This will build up foundations for…
Hodge-Iwasawa Theory II
Xin Tong
We continue our study on the Hodge-Iwasawa theory which is a continuation of our previous work on Hodge-Iwasawa theory, which is aimed at higher dimensional deformation of higher d…
Hodge-Iwasawa Theory I
Xin Tong
In this paper, we are going to establish a simultaneous generalization of the relative Iwasawa theory proposed by Kedlaya-Pottharst and the relative -adic Hodge theory after Ked…