3 citations · 3 across the 6 of their papers we have counts for
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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…
The -relative Pólya groups and -Ostrowski quotients of number fields
Ehsan Shahoseini, Abbas Maarefparvar
Let be a finite extension of number fields and be a finite set of primes of , including all the archimedean ones. In this paper, using some results of González-Avilés…
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…
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…
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…
Ostrowski quotients for finite extensions of number fields
Ehsan Shahoseini, Ali Rajaei, Abbas Maarefparvar
For a finite Galois extension of number fields, the relative Pólya group $\Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in . In this paper, usin…