Topic
Embedding problem
About: Embedding problem is a research topic. Over the lifetime, 2873 publications have been published within this topic receiving 48403 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 2003
TL;DR: In this paper, a large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, inverse problem and linear differential equations in positive characteristic.
Abstract: Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.
A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used.
This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.
1,094 citations
TL;DR: In this paper, the authors extend the results of [CHT] by removing the minimal ramification condition on the lifts and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension.
Abstract: We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.
521 citations
374 citations
TL;DR: In this paper, it was shown that a two-dimensional p-adic Galois representation which is residually modular and potentially Barsotti-Tate at p is modular under mild conditions.
Abstract: We prove that, under some mild conditions, a two dimensional p-adic Galois representation which is residually modular and potentially Barsotti-Tate at p is modular. This provides a more conceptual way of establishing the Shimura-Taniyama-Weil conjecture, especially for elliptic curves which acquire good reduction over a wildly ramified extension of ℚ 3 . The main ingredient is a new technique for analyzing flat deformation rings. It involves resolving them by spaces which parametrize finite flat group scheme models of Galois representations. Introduction.
369 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 7 |
| 2024 | 9 |
| 2023 | 26 |
| 2022 | 73 |
| 2021 | 18 |
| 2020 | 28 |