# Adequacy Condition - Explore the Science & Experts | ideXlab

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### Yamauchi Takuya – One of the best experts on this subject based on the ideXlab platform.

• ##### Serre weights for $GSp_4$ over totally real fields
, 2021
Co-Authors: Yamauchi Takuya
Abstract:

We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overline{\rho}:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ for any totally real field $F$ and any rational prime $p>2$ under the Adequacy Condition by using automorphic lifting techniques developed by Barnet-Lamb, Gee, Geraghty, and Taylor. As an application, when $p$ is split completely in $F$, we prove a variant of Serre’s weight conjecture for $\overline{\rho}$. The formulation of our Serre conjecture is done by following Toby Gee’s philosophy. Applying these results to the case when $F=\mathbb{Q}$ with a detailed study of potentially diagonalizable, crystalline lifts with some prescribed properties, we also define classical (naive) Serre’s weights. This weight would be the minimal weight among possible classical weights in some sense which occur in candidates of holomorphic Siegel Hecke eigen cusp forms of degree 2 with levels prime to $p$. The main task is to construct a potentially ordinary automorphic lift for $\overline{\rho}$ by assuming only the Adequacy Condition. The main theorems in this paper also extend many results obtained by Barnet-Lamb, Gee and Geraghty for potentially ordinary lifts and Gee and Geraghty for companion forms.Comment: 60 pages, some errors are fixed. Examples for the classical Serre weights and some description (Theorem 1.5) for companion forms are also adde

### Takuya Yamauchi – One of the best experts on this subject based on the ideXlab platform.

• ##### Serre weights for $GSp_4$ over totally real fields
arXiv: Number Theory, 2020
Co-Authors: Takuya Yamauchi
Abstract:

We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overline{\rho}:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\overline{\mathbb{F}}_p)$ for any totally real field $F$ and any rational prime $p>2$ under Adequacy Condition by using automorphic lifting techniques developed by Barnet-Lamb, Gee, Geraghty, and Taylor. As an application, when $p$ is split completely in $F$, we prove a variant of Serre’s weight conjecture for $\overline{\rho}$. The formulation of our Serre conjecture is done by following Toby Gee’s philosophy. Applying these results to the case when $F=\mathbb{Q}$ with a detailed study of potentially diagonalizable, crystalline lifts with some prescribed properties, we also define classical (naive) Serre’s weights. This weight would be the minimal weight among possible classical weights in some sense which occur in candidates of holomorphic Siegel Hecke eigen cusp forms of degree 2 with levels prime to $p$. The main task is to construct a potentially ordinary automorphic lift for $\overline{\rho}$ by assuming only the Adequacy Condition. The main theorems in this paper also extend many results obtained by Barnet-Lamb, Gee and Geraghty for potentially ordinary lifts and Gee and Geraghty for companion forms.

### Sri Dewi Sujiati – One of the best experts on this subject based on the ideXlab platform.

• ##### ANALISIS PERBANDINGAN KECUKUPAN MODAL ANTARA PT BANK NEGARA INDONESIA PERSERO TBK DAN PT BANK CENTRAL ASIA TBK
, 2007
Co-Authors: Sri Dewi Sujiati
Abstract:

The research at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk used case study, titled “Comparison Analysis of Capital Adequacy between PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk. This research aimed to find out the capital Adequacy Condition at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006 and to compare CAR at PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006, also stated which bank have better capital Condition. Data used was secondary data. Data was owed from three-monthly report of PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk by documentation method. Analysis tool to determine Capital Adequacy was Capital Adequacy Ratio (CAR). The result from PT Bank Negara Indonesia Persero Tbk and PT Bank Central Asia Tbk year 2004 to 2006 showed that capital Adequacy at both bank were enough, since Capital Adequacy Ratio (CAR) both bank were above minimum limit stated, that was 8%. PT Bank Negara Indonesia Persero Tbk CAR year 2004 per March was 19,13%, per June was 19,88%, per September was 18,48%, and December was 17,13%. CAR PT Bank Negara Indonesia Persero Tbk year 2005 per March was 18,42%, per June was 15,98%, per September was 15,52%, per December was 15,99%. PT Bank Negara Indonesia Persero Tbk CAR year 2006 per March was 190,45%, per June was 19,04%, per September was 16,95%, per December was 15,30% PT Bank Central Asia Tbk CAR year 2004 per March was 30,53%, per June was 28,65%, per September was 25,84%, per December was 23,95%. PT Bank Central Asia Tbk CAR year 2005 per March was 26,64%, per June was 25,14%, per September was 22,21%, per December was 21,53% PT Bank Central Asia Tbk CAR year 2006 per March was 25,11%, per June was 23,70%, per September 23,86%, per December was 22,09%. From both bank, capital Adequacy of PT Bank Central Asia Tbk was better than capital Adequacy of PT Bank Negara Indonesia Persero Tbk, from three monthlies period.