Deformations and elements of deformation theory

TL;DR

This paper provides an elementary overview of deformation theory for varieties, schemes, and manifolds, highlighting recent advances and applications to local/global shtukas and Newton polygons of p-divisible groups.

Contribution

It reviews novel results in deformation theory related to local shtukas, Anderson-modules, and Newton polygons, emphasizing recent developments.

Findings

Introduction to deformation theory concepts and applications

Review of recent results in local and global shtukas

Insights into deformations of p-divisible groups with specific Newton polygons

Abstract

This article consisted of an elementary introduction to deformation theory of varieties, schemes and manifolds, with some applications to local and global shtukas and fever to Newton polygons of $p$-divisible groups . Soft problems and results mainly are considered. In the framework we give review of some novel results in the theory of local shtukas, Anderson-modules, global shtukas, Newton polygons of $p$-divisible groups and on deformations of $p$-divisible groups with given Newton polygons.