Emil Artin and Helmut Hasse, G?nther Frei; Franz Lemmermeyer; Peter J. Roquette

Автор: Gatto
Название: Hasse-Schmidt Derivations on Grassmann Algebras
ISBN: 3319318411 ISBN-13(EAN): 9783319318417
Издательство: Springer
Рейтинг:
Цена: 10760.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Pl?cker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.

Автор: Gerhard Frey
Название: On Artin`s Conjecture for Odd 2-dimensional Representations
ISBN: 3540583874 ISBN-13(EAN): 9783540583875
Издательство: Springer
Рейтинг:
Цена: 4890.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: The objective of this study is to develop efficient algorithms with which to verify Artin's conjecture for odd two-dimensional representations. It is hoped that the algorithms developed for this text can also be used to solve other problems related to modular forms.

Автор: Asher Auel; Brendan Hassett; Anthony V?rilly-Alvar
Название: Brauer Groups and Obstruction Problems
ISBN: 3319468510 ISBN-13(EAN): 9783319468518
Издательство: Springer
Рейтинг:
Цена: 13974.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание:

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory.

Contributors:

- Nicolas Addington