title: Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction

authors: Delbourgo, Daniel

abstract: Let E/ℚ  be a semistable elliptic curve, and p ≠ 2 a prime of bad multiplicative reduction. For each Lie extension ℚ FT / ℚ with Galois group G∞ ≅ℤр ⋊ ℤ p ×, we construct p-adic L-functions interpolating Artin twists of the Hasse–Weil L-series of the curve E. Through the use of congruences, we next prove a formula for the analytic λ-invariant over the false Tate tower, analogous to Chern–Yang Lee's results on its algebraic counterpart. If one assumes the Pontryagin dual of the Selmer group belongs to the ℳℌ(G∞)-category, the leading terms of its associated Akashi series can then be computed, allowing us to formulate a non-commutative Iwasawa Main Conjecture in the multiplicative setting.

text: Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction Let E/ℚ  be a semistable elliptic curve, and p ≠ 2 a prime of bad multiplicative reduction. For each Lie extension ℚ FT / ℚ with Galois group G∞ ≅ℤр ⋊ ℤ p ×, we construct p-adic L-functions interpolating Artin twists of the Hasse–Weil L-series of the curve E. Through the use of congruences, we next prove a formula for the analytic λ-invariant over the false Tate tower, analogous to Chern–Yang Lee's results on its algebraic counterpart. If one assumes the Pontryagin dual of the Selmer group belongs to the ℳℌ(G∞)-category, the leading terms of its associated Akashi series can then be computed, allowing us to formulate a non-commutative Iwasawa Main Conjecture in the multiplicative setting.

year: 2015

title: Introduction

authors: Robertson, Jan

subjects: education

abstract: This issue of the Journal of Educational Change explores the complexity of leadership and, for and in change in schools. There is a large body of literature which focuses specifically on the influence of principal leadership and school improvement (see review by Hallinger & Heck, 1998) and increasing amounts recently that extend the focus to include governors, teachers, students and communities, as they explore leadership within change processes in schools (for example, Dimmock, 2000; Harris & Lambert, 2003). Professional learning communities and networking of leaders, nationally and internationally, working together to improve student achievement are common themes in the leadership literature today (for example, Stoll, Bolam & Collarbone 2002; Hargreaves, 2003). Distributed leadership is also a regular theme, with research indicating that it is in the ‘‘leadership practice’’ at various levels within a school, where change occurs (Harris, 2005; Spillane, 2006). A common theoretical underpinning in recent literature is that change in schools is a socio-cultural process (Sleegers, Geijsel & van den Berg, 2002; Wells, 1999; Wells & Claxton, 2002) and that it is through the interactions between members of the learning community that the construction of new knowledge takes place (Spillane, 2006). The contributions in this issue of the Journal of Educational Change focus attention on the socio-cultural nature of leadership, change and transformation in schools.

text: Introduction This issue of the Journal of Educational Change explores the complexity of leadership and, for and in change in schools. There is a large body of literature which focuses specifically on the influence of principal leadership and school improvement (see review by Hallinger & Heck, 1998) and increasing amounts recently that extend the focus to include governors, teachers, students and communities, as they explore leadership within change processes in schools (for example, Dimmock, 2000; Harris & Lambert, 2003). Professional learning communities and networking of leaders, nationally and internationally, working together to improve student achievement are common themes in the leadership literature today (for example, Stoll, Bolam & Collarbone 2002; Hargreaves, 2003). Distributed leadership is also a regular theme, with research indicating that it is in the ‘‘leadership practice’’ at various levels within a school, where change occurs (Harris, 2005; Spillane, 2006). A common theoretical underpinning in recent literature is that change in schools is a socio-cultural process (Sleegers, Geijsel & van den Berg, 2002; Wells, 1999; Wells & Claxton, 2002) and that it is through the interactions between members of the learning community that the construction of new knowledge takes place (Spillane, 2006). The contributions in this issue of the Journal of Educational Change focus attention on the socio-cultural nature of leadership, change and transformation in schools.

year: 2006

title: Māori and Pacific language data in linguistics classes

authors: Barbour, Julie Renee

abstract: Māori and Pacific language data rarely appears in introductory linguistic text books. In a discipline with a dearth of Māori and Pacific scholars, there is an opportunity to reflect on our teaching materials and consider ways in which we can make our classes more inclusive spaces. In this presentation, we share some of the materials and associated activities that we incorporate into undergraduate linguistics classes, in an effort to make our disciplinary content more attractive to students who join our classes with a variety of heritage languages.

text: Māori and Pacific language data in linguistics classes Māori and Pacific language data rarely appears in introductory linguistic text books. In a discipline with a dearth of Māori and Pacific scholars, there is an opportunity to reflect on our teaching materials and consider ways in which we can make our classes more inclusive spaces. In this presentation, we share some of the materials and associated activities that we incorporate into undergraduate linguistics classes, in an effort to make our disciplinary content more attractive to students who join our classes with a variety of heritage languages.

year: 2023