Algebraic and Arithmetic Theory of Quadratic Forms
About this Title
Ricardo Baeza, John S. Hsia, Bill Jacob and Alexander Prestel, Editors
This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile).
The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics.
The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory.
The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Table of Contents
- Roberto Aravire and Bill Jacob – The Milnor sequence for $W_q\scr F(x)$ in characteristic 2 when $\scr F$ is perfect [MR 2058664]
- Luis Arenas-Carmona – Spinor norm for local skew-Hermitian forms [MR 2058665]
- Paul Balmer – An introduction to triangular Witt groups and a survey of applications [MR 2058666]
- Wai Kiu Chan, A. G. Earnest and Byeong-Kweon Oh – Regularity properties of positive definite integral quadratic forms [MR 2058667]
- Wai Kiu Chan and Maria Ines Icaza – Effective results on representations of quadratic forms [MR 2058668]
- Wai Kiu Chan and Meinhard Peters – Quaternary quadratic forms and Hilbert modular surfaces [MR 2058669]
- M. Dickmann and A. Petrovich – Real semigroups and abstract real spectra. I [MR 2058670]
- Mark Gaulter – The role of characteristic vectors in the neighbour lattice process [MR 2058671]
- Larry J. Gerstein – On representation by quadratic $\Bbb F_q[x]$-lattices [MR 2058672]
- Detlev W. Hoffmann – Diagonal forms of degree $p$ in characteristic $p$ [MR 2058673]
- Donald G. James – Local densities and the representations of an integer by a definite quadratic form [MR 2058674]
- Max Karoubi – Periodicity of Hermitian $K$-theory and Milnor’s $K$-groups [MR 2058675]
- Nikita A. Karpenko – Third proof of second gap in dimensions of quadratic forms from $I^n$ [MR 2058676]
- Myung-Hwan Kim – Recent developments on universal forms [MR 2058677]
- Winfried Kohnen – Special Siegel modular forms and singular series polynomials of quadratic forms [MR 2058678]
- Ahmed Laghribi – Quasi-hyperbolicity of totally singular quadratic forms [MR 2060200]
- David B. Leep and Tara L. Smith – Witt kernels of triquadratic extensions [MR 2060201]
- David W. Lewis – Anti-automorphisms of the second kind [MR 2060202]
- Jacques Martinet – Reduction modulo 2 and 3 of Euclidean lattices. II [MR 2060203]
- M. Marshall – The elementary type conjecture in quadratic form theory [MR 2060204]
- Albrecht Pfister – On Hilbert’s theorem about ternary quartics [MR 2060205]
- Rainer Schulze-Pillot – Representation by integral quadratic forms—a survey [MR 2060206]
- Rainer Schulze-Pillot and Fei Xu – Representations by spinor genera of ternary quadratic forms [MR 2060207]
- Takao Watanabe – A survey and a complement of fundamental Hermite constants [MR 2060208]