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Algebra and Number Theory
Edited by: Rajat Tandon, University of Hyderabad, India
A publication of Hindustan Book Agency.
Hindustan Book Agency
2005; 414 pp; hardcover
ISBN-10: 81-85931-57-7
ISBN-13: 978-81-85931-57-9
List Price: US$66
Member Price: US$52.80
Order Code: HIN/23
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This volume contains refereed and updated versions of papers presented at the International Conference on Algebra and Number Theory held on the occasion of the silver jubilee of the School of Mathematics and Computer/Information Science at the University of Hyderabad (India). There are three survey articles on topics as disparate as the cyclicity problem for division algebras, Ramanujan graphs and supplementary zeroes of \(p\)-adic L functions of modular forms. There are three articles that announce results and eighteen original contributions.

The section on algebra centers on recent work on quadratic forms and division algebras, though there are also papers on modules of Witt vectors, the Hodge-Tate conjecture, Calabi-Yau manifolds, and moduli stacks of vector bundles.

The section on number theory centers on automorphic forms and representations. However, here again, there are papers on other themes pertaining to elliptic curves and transcendental number theory.

This volume is suitable for young researchers, especially those interested in recent developments in the theory of quadratic and automorphic forms and representations.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in algebra, algebraic geometry, and number theory.

Table of Contents

Part I - Algebra
  • J.-L. Colliot-Thélène -- Fields of cohomological dimension one versus \(C_1\)-fields
  • F. Ischebeck and V. Kokot -- Modules of Witt vectors
  • B. Kahn -- On "horizontal" invariants attached to quadratic forms
  • L. Cardorin, M.-A. Knus, and M. Rost -- On the dimension and other numerical invariants of invariants of algebras and vector products
  • I. Panin -- Purity for multipliers
  • W. Raskind -- A generalized Hodge-Tate conjecture for algebraic varieties with totally degenerate reduction over \(p\)-adic fields
  • D. J. Saltman -- The cyclicity question
  • F. Neumann and U. Stuhler -- Modulii stacks of vector bundles and Frobenius morphisms
  • R. Parimmala and V. Suresh -- On the length of a quadratic form
  • L. H. Rowen, A. S. Sivatski, and J.-P. Tignol -- Division algebras over rational function fields in one variable
Part II - Number Theory
  • U. K. Anandavardhanan -- Distinguished non-archimedian representations
  • P. Colmez -- Zéros supplémentaires de fonctions \(Lp\)-adiques de formes modulaires
  • T. Geisser -- The cyclotomic trace map and values of zeta functions
  • E. Ghate -- Ordinary forms and their local Galois representations
  • J. Hakim -- Supercuspidal representations and symmetric spaces
  • K. F. Lai and C. L. Zhao -- Overconvergent \(p\)-adic Siegel modular forms
  • V. K. Murty -- Splitting of abelian varieties: a new local global problem
  • M. R. Murty -- Ramanujan graphs and zeta functions
  • C. S. Rajan -- Recovering modular forms and representations from tensor and symmetric powers
  • K. Paranjpe and D. Ramakrishnan -- Quotients of \(En\) by a \(n+1\) and Calabi-Yau manifolds
  • K. Hiraga and H. Saito -- On restriction of admissible representations
  • J. Coates and R. Sujatha -- Fine Selmer groups for elliptic curves with complex multiplication
  • M. Waldschmidt -- Variations on the Six Exponential Theorem
  • H. Shiga -- Appendix: Periods on the Kummer surface
  • T. Kashio and H. Yoshida -- On the \(p\)-adic absolute \(CM\)-period symbol
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