论文标题
明确的非戈尔列施泰因r = t通过等级边界I：变形理论
Explicit non-Gorenstein R=T via rank bounds I: Deformation theory
论文作者
论文摘要
Ribet证明了关于剩余的剩余降低的GALOIS表示的非最佳水平的显着结果。我们专注于非最佳水平$ n $，它是两个不同的素数的产物，而Galois变形环预计不会是Gorenstein。我们证明，变形环的GALOIS理论标准尽可能小 - 也就是说，要有一个独特的级别$ n $的新形式，并具有降低的剩余表示。当满足此标准时，我们推断出$ r = \ mathbb {t} $定理。
Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level $N$ that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. We prove a Galois-theoretic criterion for the deformation ring to be as small as possible -- that is, for there to be a unique newform of level $N$ with reducible residual representation. When this criterion is satisfied, we deduce an $R=\mathbb{T}$ theorem.
