Rob de Jeu

James Dominic Lewis

Varieties with very little transcendental cohomology by D. Arapura $\mathcal{E}$-factors for the period determinants of curves by A. Beilinson Hodge cohomology of invertible sheaves by H. Esnault and A. Ogus Arithmetic intersection theory on Deligne-Mumford stacks by H. Gillet Notes on the biextension of Chow groups by S. Gorchinskiy Demonstration geometrique du theoreme de Lang-Neron et formules de Shioda-Tate by B. Kahn Surjectivity of the cycle map for Chow motives by S.-i. Kimura On codimension two subvarieties in hypersurfaces by N. M. Kumar, A. P. Rao, and G. V. Ravindra Smooth motives by M. Levine Cycles on varieties over subfields of $\mathbb{C}$ and cubic equivalence by J. D. Lewis Euler characteristics and special values of zeta-functions by S. Lichtenbaum Local Galois symbols on $E\times E$ by J. Murre and D. Ramakrishnan Semiregularity and Abelian varieties by V. K. Murty Chern classes, $K$-theory and Landweber exactness over nonregular base schemes by N. Naumann, M. Spitzweck, and P. A. Ostvaer Adams operations and motivic reduced powers by V. Snaith Chow forms, Chow quotients and quivers with superpotential by J. Stienstra

A Celebration in Honour of Spencer J. Bloch

Motives and Algebraic Cycles

Noriko Yui

The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.

Calabi-Yau Varieties and Mirror Symmetry

Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic $K$-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.

James Dominic Lewis

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