In this thesis, we study the compatibility between local and global Langlands correspondences for \(GL_n\). This generalizes the compatibility between local and global class field theory and is related to deep conjectures in algebraic geometry and harmonic analysis, such as the Ramanujan-Petersson conjecture and the weight monodromy conjecture. Let L be a CM field. We consider the case when \(\Pi\) is a cuspidal automorphic representation of \(GL_n(\mathbb{A}_L^\infty)\), which is conjugate self-dual and regular algebraic. Under these assumptions, there is an l-adic Galois representation \(R_l(\Pi)\) associated to \(\Pi\), which is known to be compatible with the local Langlands correspondence in most cases (for example, when n is odd) and up to semisimplification in general. In this thesis, we complete the proof of the compatibility when \(l \neq p\) by identifying the monodromy operator N on both the local and the global sides. On the local side, the identification amounts to proving the Ramanujan-Petersson conjecture for \(\Pi\) as above. On the global side it amounts to proving the weight-monodromy conjecture for part of the cohomology of a certain Shimura variety. / Mathematics

The performance of eleven 'Valencia Late' and nine 'Washington Navel' orange (Citrus sinensis) clones all on rough lemon (Citrus jambhiri) rootstock was evaluated. Significant differences in trunk cross sectional area, plant canopy volume, cumulative yield and yield efficiency were found between clones of different citrus cultivars. Some clones such as VL106, VL139, VL185 and WN204 appeared to be promising in terms of good growth characteristics and high yield, and could therefore be used for the national performance trials. Studies on post-harvest degreening of 'Valencia Late' oranges were also carried out at Matuga Regional Research Sub-Centre (Kenya) in a series of experiments. Fully mature fruits were dipped for three minutes in 0, 500, 1000, 1500, 2000, 2500 and 3000 ppm concentrations of ethephon. Fruits wrapped in aluminum foil shrivelled less and retained their firmness and freshness. Rind brightness increased by dipping of fruits in ethephon (2000) ppm giving a good colour change. Dipping fruits a second time three days after the first dip did not have any significant effect on colour change. (Chemical names used: (2-Chloroethyl)phosphonic acid (ethephon).

Soybean growth with respect to N fertilizer rates, plant population densities and two cultivars was investigated on three Quebec soils at four sites. Soybean nodulation, growth, grain yields and nutrient uptake at three developmental stages were investigated. Soil nitrate levels after harvest were also studied. / N fertilizer application depressed soybean nodulation consistently, but improved soybean growth where initial soil nitrate levels were low. Grain yield was increased at one site with added N, where soybean growth was stressed by low initial soil nitrate levels (below 17 kg N/ha) and severe summer drought. Soybean N and K uptake were increased with increased N fertilizer but P uptake was not affected. Residual soil nitrate content in the 0-50 cm depth in the fall of the crop year increased linearly and this effect carried over to the following spring. / Plant population had little effect on individual plant nodulation but increased fresh nodule mass per unit area. Plant biomass, grain yield and nutrient uptake were increased with increased population densities. / The cultivar Apache had better nodulation potential and grain yield potential and was better adapted to intensive management practices with high plant populations than the cultivar Maple-Arrow.

This study adopts a comparative institutional approach to address the question of why corporate social performance (CSP) tends to vary cross-nationally. Using a sample of 1551 firms from 20 different countries, I test the relationships between key institutional variables suggested in the varieties of capitalism literature (see Hall & Soskice, 2001) and corporate social performance. Specifically, I test the relationships between coordination in corporate governance and labour relations and CSP. To provide a comprehensive measure of CSP, I separately measure different dimensions of CSP (social and environmental) and categories of CSP(processes and outcomes). The results indicated that the market economy firms are embedded within produces differences in how they perform on social and environmental dimensions. In particular, national level coordination in corporate governance was found to produce differences in both the processes firms adopt to address social and environmental issues and the outcomes and impacts of firm actions on social and environmental dimensions. These institutional factors were found to be stronger predictors of CSP than both cultural differences and differences in industry composition. The results of this study lend support to the argument that CSP is driven by institutions at the national-level. I discuss the implications of these findings and chart out a course for futureresearch in the area.

This study adopts a comparative institutional approach to address the question of why corporate social performance (CSP) tends to vary cross-nationally. Using a sample of 1551 firms from 20 different countries, I test the relationships between key institutional variables suggested in the varieties of capitalism literature (see Hall & Soskice, 2001) and corporate social performance. Specifically, I test the relationships between coordination in corporate governance and labour relations and CSP. To provide a comprehensive measure of CSP, I separately measure different dimensions of CSP (social and environmental) and categories of CSP(processes and outcomes). The results indicated that the market economy firms are embedded within produces differences in how they perform on social and environmental dimensions. In particular, national level coordination in corporate governance was found to produce differences in both the processes firms adopt to address social and environmental issues and the outcomes and impacts of firm actions on social and environmental dimensions. These institutional factors were found to be stronger predictors of CSP than both cultural differences and differences in industry composition. The results of this study lend support to the argument that CSP is driven by institutions at the national-level. I discuss the implications of these findings and chart out a course for futureresearch in the area.

The main topic of this thesis is the tropicalizations of Severi varieties, which we call tropical Severi varieties. Severi varieties are classical objects in algebraic geometry. They are parameter spaces of plane nodal curves. On the other hand, tropicalization is an operation defined in tropical geometry, which turns subvarieties of an algebraic torus into certain polyhedral objects in real vector spaces. By studying the tropicalizations, it may be possible to transform algebro-geometric problems into purely combinatorial ones. Thus, it is a natural question, “what are tropical Severi varieties?” In this thesis, we give a partial answer to this question: we obtain a description of tropical Severi varieties in terms of regular subdivisions of polygons. Given a regular subdivision of a convex lattice polygon, we construct an explicit parameter space of plane curves. This parameter space is a much simpler object than the corresponding Severi variety and it is closely related to a flat degeneration of the Severi variety, which in turn describes the tropical Severi variety. We present two applications. First, we understand G.Mikhalkin’s correspondence theorem for the degrees of Severi varieties in terms of tropical intersection theory. In particular, this provides a proof of the independence of point-configurations in the enumeration of tropical nodal curves. The second application is about Secondary fans. Secondary fans are purely combinatorial objects which parameterize all the regular subdivisions of polygons. We provide a relation between tropical Severi varieties and Secondary fans.

Doctor of Philosophy / The Hecke character of an abelian variety A/F is an isogeny invariant and the Galois action is such that A is isogenous to its Galois conjugate A^σ if and only if the corresponding Hecke character is fixed by σ. The quadratic twist of A by an extension L/F corresponds to multiplication of the associated Hecke characters. This leads us to investigate the Galois groups of families of quadratic extensions L/F with restricted ramification which are normal over a given subfield k of F. Our most detailed results are given for the case where k is the field of rational numbers and F is a field of definition for an elliptic curve with complex multiplication by K. In this case the groups which occur as Gal(L/K) are closely related to the 4-torsion of the class group of K. We analyze the structure of the local unit groups of quadratic fields to find conditions for the existence of curves with good reduction everywhere. After discussing the question of finding models for curves of a given Hecke character, we use twists by 3-torsion points to give an algorithm for constructing models of curves with known Hecke character and good reduction outside 3. The endomorphism algebra of the Weil restriction of an abelian variety A may be determined from the Grössencharacter of A. We describe the computation of these algebras and give examples in which A has dimension 1 or 2 and its Weil restriction has simple abelian subvarieties of dimension ranging between 2 and 24.

Doctor of Philosophy (PhD) / Changing the behaviour of firms to take environmental concerns into account is seen as unlikely without effective regulations. However, corporations are increasingly keen to represent themselves as ‘green’, including those in the world’s largest manufacturing sector: the car industry. Given rising concern for the environment and environmental sustainability since the 1990s this thesis asks: what motivates car firms to actually make environmental commitments? Answering this question has implications for whether these commitments are ‘real’ and if so whether they are occurring in response to material factors (e.g. state regulations and consumer demand) versus normative factors (e.g. social attitudes and internal company strategies). In order to answer it, the thesis applies the insights of the institutional varieties of capitalism approach to the German, United States and Japanese car industries, and specific firms within them, in respect of the environmental issue of climate change from 1990 to 2004. Empirical national data is analysed, as well the environmental reporting of individual firms and interviews with key personnel. The main findings are that what leads the car industry to see environmental issues as central to their business interests hinges on the impact of differing national institutional factors. Specifically, it is a matter of whether firms have a liberal market economy (LME) as their home base, in the case of US firms, or a coordinated market economy (CME) as their home base, in the case of German and Japanese firms. US car firms react more to the material imperatives of consumer demand and state regulations. German and Japanese firms are more mindful of normative factors for their initiatives, such as social attitudes (especially for German firms) and internal company strategies (especially for Japanese firms). They have more of a partnership approach with government. Therefore, car firms have very distinct ‘lenses’ through which they see the environmental performance of the cars they produce. As such, the thesis concludes that the variety of capitalism of nations has implications not just for the type of products that economic actors such as car firms produce, and the competitive advantages they develop, but also the way they address related issues arising as a result of their activities, including environmental issues.

Doctor of Philosophy / The Hecke character of an abelian variety A/F is an isogeny invariant and the Galois action is such that A is isogenous to its Galois conjugate A^σ if and only if the corresponding Hecke character is fixed by σ. The quadratic twist of A by an extension L/F corresponds to multiplication of the associated Hecke characters. This leads us to investigate the Galois groups of families of quadratic extensions L/F with restricted ramification which are normal over a given subfield k of F. Our most detailed results are given for the case where k is the field of rational numbers and F is a field of definition for an elliptic curve with complex multiplication by K. In this case the groups which occur as Gal(L/K) are closely related to the 4-torsion of the class group of K. We analyze the structure of the local unit groups of quadratic fields to find conditions for the existence of curves with good reduction everywhere. After discussing the question of finding models for curves of a given Hecke character, we use twists by 3-torsion points to give an algorithm for constructing models of curves with known Hecke character and good reduction outside 3. The endomorphism algebra of the Weil restriction of an abelian variety A may be determined from the Grössencharacter of A. We describe the computation of these algebras and give examples in which A has dimension 1 or 2 and its Weil restriction has simple abelian subvarieties of dimension ranging between 2 and 24.

Thesis (M.S.)--Montana State University--Bozeman, 2004. / Typescript. Chairperson, Graduate Committee: Janice G. P. Bowman. Includes bibliographical references (leaves 47-51).