تقرير
On the existence of analytic families of stable lattices in trianguline representations and their reductions
العنوان: | On the existence of analytic families of stable lattices in trianguline representations and their reductions |
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المؤلفون: | Torti, Emiliano |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Number Theory, 11F80, , 11F85, 14G20, 11F03 |
الوصف: | In this article, we prove the existence of rigid analytic families of $G$-stable lattices with locally constant reductions inside families of representations of a topologically compact group $G$, extending a result of Hellman obtained in the semi-simple residual case. Implementing this generalization in the context of Galois representations, we prove a local constancy result for reductions modulo prime powers of trianguline representations of generic dimension $d$. Moreover, we present two explicit applications. First, in dimension two, we extend to a prime power setting and to the whole rigid projective line a recent result of Bergdall, Levin and Liu concerning reductions of semi-stable representations of $\text{Gal}(\overline{\mathbb{Q}}_p / \mathbb{Q}_p)$ with fixed Hodge-Tate weights and large $\mathcal{L}$-invariant. Second, in dimension $d$, let $V_n$ be a sequence of crystalline representations converging in a certain geometric sense to a crystalline representation $V$. We show that for any refined version $(V, \sigma)$ of $V$ (or equivalently for any chosen triangulation of its attached $(\varphi, \Gamma)$-module $D_{\text{rig}} (V)$ over the Robba ring), there exists a sequence of refinement $\sigma_n$ of each of the $V_n$ such that the limit as refined representations $(V_n , \sigma_n )$ converges to the $(V, \sigma)$. This result does not hold under the weaker assumption that $V_n$ converges only uniformly $p$-adically to $V$ (in the sense of Chenevier, Khare and Larsen). |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2401.00462 |
رقم الأكسشن: | edsarx.2401.00462 |
قاعدة البيانات: | arXiv |
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