Tropical Dolbeault Cohomology of Non-archimedean Spaces
نویسنده
چکیده
In this survey article, we discuss some recent progress on tropical Dolbeault cohomology of varieties over non-Archimedean fields, a new cohomology theory based on real forms defined by Chambert-Loir and Ducros.
منابع مشابه
Tropical Cycle Classes for Non-archimedean Spaces and Weight Decomposition of De Rham Cohomology Sheaves
This article has three major goals. First, we define tropical cycle class maps for smooth varieties over non-Archimedean fields, valued in the Dolbeault cohomology defined in terms of real forms introduced by Chambert-Loir and Ducros. Second, we construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over certain non-Archimedea...
متن کاملMonodromy Map for Tropical Dolbeault Cohomology
We define monodromy maps for tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields. We propose a conjecture of Hodge isomorphisms via monodromy maps, and provide some evidence.
متن کاملDolbeault Cohomology of a Loop Space
Loop spaces LM of compact complex manifolds M promise to have rich analytic cohomology theories, and it is expected that sheaf and Dolbeault cohomology groups of LM will shed new light on the complex geometry and analysis of M itself. This idea first occurs in [W], in the context of the infinite dimensional Dirac operator, and then in [HBJ] that touches upon Dolbeault groups of loop spaces; but...
متن کاملSuperstability of $m$-additive maps on complete non--Archimedean spaces
The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.
متن کاملStability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces
In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.
متن کامل