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 Tata Institute of Fundamental Research 2002; 651 pp; hardcover ISBN-10: 81-7319-476-9 ISBN-13: 978-81-7319-476-4 List Price: US$65 Member Price: US$52 Order Code: TIFR/5 This volume contains papers by invited speakers at the International Colloquium on Algebra, Arithmetic and Geometry, held at the Tata Institute of Fundamental Research (Mumbai, India) in January 2000. The articles present the latest developments in a broad variety of topics from algebraic geometry, group theory, and $$K$$-theory. It is suitable for graduate students and research mathematicians interested in those areas. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. Readership Graduate students and research mathematicians interested in algebraic geometry, algebraic group theory, and algebraic $$K$$-theory. Table of Contents Part I S. S. Abhyankar -- Symplectic groups and permutation polynomials L. L. Avramov and S. Iyengar -- Homological criteria for regular homomorphisms and for locally complete intersection homomorphisms P. Barquero and A. Merkurjev -- Norm principle for reductive algebraic groups S. M. Bhatwadekar and R. Sridharan -- On Euler classes and stably free projective modules J. Biswas, G. Dayal, K. H. Paranjape, and G. V. Ravindra -- Higher Abel-Jacobi maps S. Bloch and V. Srinivas -- Enriched Hodge structures J.-L. Colliot-Thélène, M. Ojanguren, and R. Parimala -- Quadratic forms over fraction fields of two-dimensional Henselian rings and Brauer groups of related schemes E. M. Friedlander and M. E. Walker -- Semi-topological $$K$$-theory of real varieties Part II J. Herzog and E. Sbarra -- Sequentially Cohen-Macaulay modules and local cohomology W. van der Kallen -- From Mennicke symbols to Euler class groups M.-A. Knus, R. Parimala, and R. Sridharan -- On generic triality V. B. Mehta and S. Subramanian -- On the Harder-Narasimhan filtration of principal bundles V. B. Mehta and A. J. Parameswaran -- Geometry of low height representations M. Miyanishi and K. Masuda -- Generalized Jacobian conjecture and related topics N. M. Kumar -- Construction of rank two vector bundles on projective spaces M. V. Nori -- Constructible sheaves M. P. Murthy -- Cancellation problem for projective modules over certain affine algebras V. L. Popov -- Self-dual algebraic varieties and nilpotent orbits P. C. Roberts -- Intersection multiplicities and dimension inequalities P. Russell -- Some formal aspects of the theorems of Mumford-Ramanujam R. Sujatha -- Euler-Poincaré characteristics of $$p$$-adic Lie groups and arithmetic A. Suslin -- On the vanishing of $$H_3(SL_2(A,I), \mathbb{Z}/l)$$