Ehsan Shahoseini

activity

20212026

most citedOstrowski quotients for finite extensions of number fields

3 citations · 3 across the 6 of their papers we have counts for

collaborators

8 papers

math.GN2026

Finite-Point Metrizable Coarsenings: Compatible Gauges, Simplicial Metrics, and Hausdorff Lower Bounds

Ahmad ja'afari kalvan, Ehsan Shahoseini

Let $(X, τ)$ be metrizable and let $F = {a_{1}, \dots, a_{k}} \subseteq X$ , where $2 \leq k < \infty$ . We represent all metrizable topologies $σ \subseteq τ$ agreeing with $τ$ on $X ∖ F$ …

math.GN2026

One-Point Metrizable Coarsenings: Gauges and Local Metric Preservation

Ahmad ja'afari kalvan, Ehsan Shahoseini

Let $(X, τ)$ be metrizable and let $a \in X$ . We give a constructive account of metrizable topologies $σ \subseteq τ$ that agree with $τ$ on $X ∖ {a}$ . Applying Hausdorff's cla…

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

The $S$ -relative Pólya groups and $S$ -Ostrowski quotients of number fields

Ehsan Shahoseini, Abbas Maarefparvar

Let $K / F$ be a finite extension of number fields and $S$ be a finite set of primes of $F$ , including all the archimedean ones. In this paper, using some results of González-Avilés…

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.NT2022

A criterion for perfectoid fields

Ehsan Shahoseini, Kiran S. Kedlaya

The tilting correspondence is a fundamental property of perfectoid fields. In this note, we show that the tilting construction can also be used to detect perfectoid fields among no…

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…

math.NT2021★ 3 cited

Ostrowski quotients for finite extensions of number fields

Ehsan Shahoseini, Ali Rajaei, Abbas Maarefparvar

For $L / K$ a finite Galois extension of number fields, the relative Pólya group $\Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in $L / K$ . In this paper, usin…