Images of Galois representations in mod pp Hecke algebras

Let $(\mathbb{T}_f,\mathfrak{m}_f)$ denote the mod $p$ local Hecke algebra attached to a normalised Hecke eigenform $f$, which is a commutative algebra over some finite field $\mathbb{F}_q$ of characteristic $p$ and with residue field $\mathbb{F}_q$. By a result of Carayol we know that, if the residual Galois representation $\overline{\rho}_f:G_\mathbb{Q}\rightarrow\mathrm{GL}_2(\mathbb{F}_q)$ is absolutely irreducible, then one can attach to this algebra a Galois representation $\rho_f:G_\mathbb{Q}\rightarrow\mathrm{GL}_2(\mathbb{T}_f)$ that is a lift of $\overline{\rho}_f$. We will show how one can determine the image of $\rho_f$ under the assumptions that $(i)$ the image of the residual representation contains $\mathrm{SL}_2(\mathbb{F}_q)$, $(ii)$ that $\mathfrak{m}_f^2=0$ and $(iii)$ that the coefficient ring is generated by the traces. As an application we will see that the methods that we use allow us to deduce the existence of certain $p$-elementary abelian extensions of big non-solvable number fields

Non-Abelian Berry Phase, Instantons and N=(0,4) Supersymmetry

In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations. Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R^{4n} satisfies a generalization of the self-dual Yang-Mills equations. Upon dimensional reduction, these become the tt* equations. We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.Comment: 11 page

The Role of Firm Size in Training Provision Decisions: evidence from Spain.

The level of training provided by small firms to their employees is below that provided by their larger counterparts. The provision of firm-related training is believed to be associated to certain characteristics of the firm. In this paper we argue that small firms provide fewer training opportunities as they are less likely to be associated with these characteristics than large firms. The suitability of estimating training decisions as a double-decision process is examined here: first, a firm has to decide whether to provide training or not and, second, having decided to do so, the amount of training to provide. The differences in training provision between small and large firms are decomposed in order to analyse the individual contribution of these characteristics to explaining the gap. The results show that small firms face greater obstacles in accessing training and that the main reasons for that are related to their technological activity and the geographical scope of the market in which they operate.Continuous training, Firm size, Innovative activity.

PENERAPAN MODEL PELATIHAN BERBASIS SMART DALAM LAYANAN KONSULTASI UNTUK KEMAMPUAN GURU BK MELAKSANAKAN LAYANAN KHUSUS

The teachers complained that the training that had been going on at P4TK for a week or more, and was only filled with theories that they had previously stated, while at the end, some teachers were tired and when they returned to their assignments they only brought a sheet of research. This program aims to provide training to participants in a short time in one skill training. This training uses a SMART model approach (specific, measurable, achievable, relevant, and time-bound) with the material "Consulting Services" is a counseling service by a counselor to one or more customers (consulters) if the consultants want it, which supports the consultancy gaining insight, understanding and ways that need to be applied to deal with third party issues. This model is implemented in a face-to-face format between counselors (as consultants) and customers (as consultants). The subjects of the SMART-based training are 15 BK SMP teachers in South Nias Regency. The results show that skills are an important factor that can help improve the competence of BK teachers, who participate in consultation activities specifically for students at the school as a third party

SISAL (Speleothem Isotopes Synthesis and AnaLysis Working Group) database version 1b

Note: This edition of the SISAL database was withdrawn on 13 July 2020. It has been superseded by a new edition available at http://dx.doi.org/10.17864/1947.256. Stable isotope records from speleothems provide information on past climate changes, most particularly information that can be used to reconstruct past changes in precipitation and atmospheric circulation. SISAL (Speleothem Isotope Synthesis and Analysis) is an international working group of the Past Global Changes (PAGES) project. The working group aims to provide a comprehensive compilation of speleothem isotope records for climate reconstruction and model evaluation. Version 1b of the SISAL database contains oxygen and carbon isotope measurements from 440 individual and 15 composite speleothem records from 221 cave systems worldwide, as well as metadata describing their cave settings and age-depth models. New records have been added and some metadata has been amended. The SISAL working group has also created SISAL chronologies for 20 entities, all of which had no published chronologies. In order to assure traceability, any presentation, report, or publication that uses the SISALv1b database should cite Atsawawaranunt et al. (2018) (The SISAL database: a global resource to document oxygen and carbon isotope records from speleothems; https://doi.org/10.5194/essd-10-1687-2018) and Comas-Bru et al. (2019) (Evaluating model outputs using integrated global speleothem records of climate change since the last glacial; https://doi.org/10.5194/cp-2019-25). If using individual sites or speleothems, the literature citations for published work provided in the database should also be cited. Contact information of data contributors of unpublished data is also provided and these should be contacted when unpublished records are used on an individual basis