Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures'' in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely...
Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the d...
This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of these essays. Highlighting the pervasive nature of mathematics today in different areas, the book also covers the spread of mathematical ideas and techniques in areas ranging from computer science to physics to biology.
This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will a...
The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the...
The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic fo...
We dedicate this volume to Professor Parimala on the occasion of her 60th birthday. It contains a variety of papers related to the themes of her research. Parimala's rst striking result was a counterexample to a quadratic analogue of Serre's conjecture (Bulletin of the American Mathematical Society, 1976). Her in uence has cont- ued through her tenure at the Tata Institute of Fundamental Research in Mumbai (1976-2006), and now her time at Emory University in Atlanta (2005-present). A conference was held from 30 December 2008 to 4 January 2009, at the U- versity of Hyderabad, India, to...
We dedicate this volume to Professor Parimala on the occasion of her 60th birthday. It contains a variety of papers related to the themes of her resea...
