## New AMS-Distributed Publications

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Contents: R. Meyer, Categorical aspects of bivariant K-theory; A. Bartels, S. Echterho , and W. Lück, Inheritance of isomorphism conjectures under colimits; H. Emerson and R. Meyer, Coarse and equivariant co-assembly maps; F. Muro and A. Tonks, On K_{1 }of a Waldhausen category; M. Karoubi, Twisted K-theory—old and new; C. Voigt, Equivariant cyclic homology for quantum groups;

P.

C. Rouse, A Schwartz type algebra for the tangent groupoid;

J.

Cuntz, C -algebras associated with the ax + b-semigroup over

N; W. Werner, On a class of Hilbert C -manifolds; U. Bunke, T. Schick, M. Spitzweck, and A. Thom, Duality for topological abelian group stacks and T -duality; P. Bressler, A. Gorokhovsky, R. Nest, and B. Tsygan, Deformations of gerbes on smooth manifolds; G. Garkusha and M. Prest, Torsion classes of finite type and spectra; T. Geisser, Parshin’s conjecture revisited; C. Weibel, Axioms for the norm residue isomorphism; List of contributors; List of participants.

EMS Series of Congress Reports, Volume 2

October 2008, 454 pages, Hardcover, ISBN: 978-3-03719-060-9, 2000 Mathematics Subject Classification: 19-06, 58-06, 14A22, 14Fxx, 46Lxx, 53D55, 58Bxx, AMS members US$99, List US$124, Order code EMSSCR/2

# Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology

Martin C. Olsson, University of California, Berkeley, CA

In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a p-adic field and applications to p-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the ( , N, G)-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the C_{st}-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of p-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Contents: Introduction; Divided power structures on stacks and the crystalline topos; Crystals and di erential calculus on stacks; The Cartier isomorphism and applications; De Rham–Witt theory; The abstract Hyodo–Kato isomorphism; The ( , N, G)-structure on de Rham cohomology; A variant construction of the ( , N, G)- structure; Comparison with syntomic cohomology; Comparison

with log geometry in the sense of Fontaine and Illusie; Bibliography; Index of notation; Index of terminology.

Astérisque, Number 316

September 2008, 412 pages, Softcover, ISBN: 978-2-85629-249-5, 2000 Mathematics Subject Classification: 14F20, 14F30, 14G20, 11G25, Individual member US$119, List US$132, Order code AST/316

# Trends in Representation Theory of Algebras and Related Topics

Andrzej Skowron´ski, Nicholas Copernicus University, Torun, Poland, Editor

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development.

The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen–Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander–Reiten theory, Calabi–Yau triangulated categories, Poincaré duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory.

This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Contents: S. Ariki, Finite dimensional Hecke algebras; G. Bobin´ski, C. Riedtmann, and A. Skowron´ski, Semi-invariants of quivers and their zero sets; I. Burban and Y. Drozd, Maximal Cohen–Macaulay modules over surface singularities; J. F. Carlson, Rank varieties;

K.

Erdmann and A. Skowron´ski, Periodic algebras; C. Geiss,

B.

Leclerc, and J. Schröer, Preprojective algebras and cluster

algebras; I. G. Gordon, Symplectic reflection algebras; O. Iyama, Auslander–Reiten theory revisited; P. Jørgensen, Calabi–Yau categories and Poincaré duality spaces; S. Kasjan, Representation types of algebras from the model theory point of view; B. Keller, Calabi–Yau triangulated categories; S. Koenig, A panorama of diagram algebras; H. Lenzing and J. A. de la Pen´a, Spectral analysis

80

Notices of the AMS

Volume 56 Number 1