3 papers
math.NT2025
Deformation Theory of Galois Representations and the Taylor--Wiles Method
Ehsan Shahoseini
In this chapter, we want to have an overview of the Taylor--Wiles patching method. For this purpose, at the first, we recall Mazur's theory of deforming Galois representations and…
math.NT2023
Solvable extensions of number fields ramified at only one prime are Ostrowski
Ali Rajaei, Ehsan Shahoseini
In this note, we show that, under a certain condition, solvable extensions of number fields ramifed at only one prime are Ostrowski. As a corollary, we deduce a generalization of H…
math.NT2021
An Introduction to Perfectoid Fields
Ehsan Shahoseini, Soroush Pasandideh
This survey is a final project of Twopole DRP in fall 20201. In this paper we try to understand a tiny part of the vast theory of perfecoid spaces, called perfectoid fields. We sta…