newpubs-jun-jul98.qxp 5/18/98 11:28 AM Page 761 New Publications Offered by the AMS Higher Initial Ideals Algebra and Algebraic EMOIRS M of the American Mathematical Society of Homogeneous Geometry Volume 134 Number 638 Ideals Higher Initial Ideals Gunnar Fløystad, University of On Stability and of Homogeneous Ideals EMOIRS Gunnar Fløystad Bergen, Norway M of the American Mathematical Society Endoscopic Transfer THEMAT Volume 134 Number 635 A IC M A Given a homogeneous ideal I and a L N ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ A S O C I C R I E E ΑΓΕΩΜΕ T M Y A F OU 88 NDED 18 monomial order, one may form the On Stability and of Unipotent Orbital Endoscopic Transfer of initial ideal in(I). The initial ideal American Mathematical Society Unipotent Orbital Integrals Integrals on p-adic gives information about I, for on p-adic Symplectic Groups instance I and in(I) have the same Magdy Assem Symplectic Groups Hilbert function. However, if is the THEMAT A IC M A ΤΡΗΤΟΣ ΜΗ L I N ΕΙΣΙΤΩ A S O C I C R I E E ΑΓΕΩΜΕ T M Y Magdy Assem sheafification of I one cannot read the higher cohomological A F OU 88 NDED 18 dimensions hi (Pn, (ν)) from in(I). This work remedies this by The theory of endoscopy is an I American Mathematical Society defining a series of higher initial ideals ins (I) for s 0. Each ≥ intriguing part of the Langlands cohomological dimension hi (Pn, (ν)) may be read from the program, as it provides a way to I ins (I). The ins (I) are however more refined invariants and attack the functoriality principle of contain considerably more information about the ideal I. Langlands for certain pairs of reductive groups (G, H), in which H is what is known as an endoscopic group for G. The This work considers in particular the case where I is the 3 starting point for this method is a close study of the relation- homogeneous ideal of a curve in P and the monomial order is ship of orbital integrals on G with stable orbital integrals on reverse lexicographic. Then the ordinary initial ideal in0(I) and H. the higher initial ideal in1(I) have very simple representations in the form of plane diagrams. This volume investigates unipotent orbital integrals of spher- ical functions on p-adic symplectic groups. The results are Features: then put into a conjectural framework, that predicts (for split • enables one to visualize cohomology of projective schemes n classical groups) which linear combinations of unipotent in P orbital integrals are stable distributions. • provides an algebraic approach to studying projective schemes Contents: Introduction; Unipotent orbits and prehomogeneous • gives structures which are generalizations of initial ideals spaces; The Hecke algebra and some Igusa local orbital zeta functions; The evaluation of f H at the identity; Matching of Contents: Introduction; Borel-fixed ideals; Monomial orders; unipotent orbital integrals; Remarks on stability and endo- Some algebraic lemmas; Defining the higher initial ideals; s+1 scopic transfer; Appendix I; Appendix II; References. Representing the higher initial ideals; Group action on R (I); Describing the action on Rs+1(I); Borel-fixedness; Higher initial Memoirs of the American Mathematical Society, Volume 134, ideals of hyperplane sections; Representing the higher initial Number 635 ideals of general hyperplane sections; Higher initial ideals as July 1998, 101 pages, Softcover, ISBN 0-8218-0765-X, LC 98- combinatorial structures; Reading cohomological information; 18262, 1991 Mathematics Subject Classification: 22E35, 22E50, Examples: Points and curves in P3; References. Individual member $24, List $40, Institutional member $32, Memoirs of the American Mathematical Society, Volume 134, Order code MEMO/134/635N Number 638 July 1998, 68 pages, Softcover, ISBN 0-8218-0853-2, LC 98- 18255, 1991 Mathematics Subject Classification: 13D25, 14H50; 13P10, 14J99, Individual member $22, List $36, Institutional member $29, Order code MEMO/134/638N JUNE/JULY 1998 NOTICES OF THE AMS 761 newpubs-jun-jul98.qxp 5/18/98 11:28 AM Page 762 New Publications Offered by the AMS Algebras and Modules I Canadian Mathematical Society Algebras and Société Mathématique du Canada Idun Reiten, Sverre O. Smalø, Modules II Canadian Mathematical Society Société Mathématique du Canada and Øyvind Solberg, Idun Reiten, Sverre O. Smalø, Norwegian University of Algebras and Modules II and Øyvind Solberg, Science and Technology, Idun Reiten Sverre O. Smalø Norwegian University of Algebras and Modules I Øyvind Solberg Trondheim, Editors Editors Idun Reiten Science and Technology, Sverre O. Smalø Øyvind Solberg Editors This volume contains recent results Trondheim, Editors CMS CONFERENCE PROCEEDINGS on geometric aspects of representa- Volume 24 tions of algebras, a thorough This volume contains 43 research CMS CONFERENCE PROCEEDINGS papers based on results presented at Volume 23 treatment of the theory of quasitilted algebras, new developments on infi- the Eighth International Conference nite dimensional representations of on Representations of Algebras (ICRA VIII) held in Geiranger, finite dimensional algebras, a bridge Norway, in 1996. The papers, written by experts in the field, between representation of algebraic groups and representation cover the most recent developments in the representation theory of finite dimensional algebras, and recent discoveries theory of artin algebras and related topics. on modular representation theory. In addition, the volume The papers cover: representation of tame, biserial, cellular, contains two papers devoted to some of Maurice Auslander’s factorial hereditary, Hopf, Koszul, non-polynomial growth, many contributions both in the representation theory of finite preprojective, Temperley-Lieb, tilted and quasitilted algebras. dimensional algebras and in commutative ring theory. The Other topics include: tilting/cotilting modules and generaliza- invited contributions to this volume are based on lectures tions as -modules, exceptional sequences of modules ∗ given by leading researchers in the field at the Workshop on and vector bundles, homological conjectures, Hochschild Representations of Algebras and Related Topics, Trondheim, cohomology, cyclic homology, homologically finite subcate- Norway, in 1996. gories, representations of posets, regular modules, vector Features: space categories, triangulated categories, moduli spaces of • a unique collection of survey papers containing old and new representations of quivers, postprojective (and preprojective) developments in the representation theory of finite dimen- partitions, stable and derived equivalences, and pure-injective, sional algebras and related topics infinite dimensional, and endofinite representations. A general • an outstanding source for examples of different techniques background in noncommutative algebra including rings, developed in recent years in this area of research modules and homological algebra is required. • papers presented with emphasis on clarity and readability Features: A general background in noncommutative algebra including • a unique source for the developments in the representation rings, modules and homological algebra is required. Given that, theory of finite dimensional and artin algebras and related parts of this volume would be suitable as a textbook for an topics advanced graduate course in algebra. • a wide variety of important papers by leading researchers in the field, with references to earlier developments in the field Members of the Canadian Mathematical Society may order at the AMS member price. Members of the Canadian Mathematical Society may order at the AMS member price. Contents: K. Bongartz, Some geometric aspects of representa- tion theory; W. Crawley-Boevey, Infinite-dimensional modules Contents: L. Angeleri-Hügel and F. U. Coelho, A note on a in the representation theory of finite-dimensional algebras; certain class of tilted algebras; H. Asashiba, Derived equiva- D. Happel, Quasitilted algebras; H. Lenzing, Auslander’s work lence and stable equivalence of repetitions of algebras of finite on artin algebras; B. Parshall, Some finite dimensional algebras global dimension; I. Assem, A. Beligiannis, and N. Marmaridis, arising in group theory; J. Rickard, Some recent advances in Right triangulated categories with right semi-equivalences; modular representation theory; Y. Yoshino, Auslander’s work Ø. Bakke, The existence of short exact sequences with some of on Cohen-Macaulay modules and recent development. the terms in given subcategories; M. J. Bardzell and E. N. Marcos, Induced boundary maps for the cohomology of Conference Proceedings, Canadian Mathematical Society, monomial and Auslander algebras; M. Barot, The repetitive Volume 23 partition of the repetitive category of a tubular algebra; June 1998, 198 pages, Softcover, ISBN 0-8218-0850-8, LC 98- A. V. Roiter, K. I. Belousov, and L. A. Nazarova, Representa- 3695, 1991 Mathematics Subject Classification: 16Gxx; 16Dxx, tions of finitely represented dyadic sets; A. B. Buan and 16Exx, 18Gxx, 20Cxx, Individual member $23, List $39, Ø. Solberg, Relative cotilting theory and almost complete Institutional member $31, Order code CMSAMS/23N cotilting modules; C. Cibils, Hochschild cohomology algebra of radical square zero algebras; R. Colpi and G. D’Este, Equiva- lences represented by faithful non-tilting -modules; ∗ T. Dana-Picard and M. Schaps, Non reduced components of Alg n; A. P. Dean and F. Okoh, Extensionless modules of infi- nite rank; B. Deng and J. Xiao, A quiver description of hereditary categories and its application to the first Weyl algebra; E. Dieterich, Power-associative