Eisenstein Cohomology for GLN and the Special Values of Rankin-Selberg L-Functions (eBook)

Gunter Harder, Anantharam Raghuram (Autoren)

eBook Download: PDF

2019
240 Seiten
Princeton University Press (Verlag)
978-0-691-19793-7 (ISBN)

Infos

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.The authors study the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL(N). The image of the global cohomology in the cohomology of the Borel-Serre boundary is called Eisenstein cohomology, since at a transcendental level the cohomology classes may be described in terms of Eisenstein series and induced representations. However, because the groups are sheaf-theoretically defined, one can control their rationality and even integrality properties. A celebrated theorem by Langlands describes the constant term of an Eisenstein series in terms of automorphic L-functions. A cohomological interpretation of this theorem in terms of maps in Eisenstein cohomology allows the authors to study the rationality properties of the special values of Rankin-Selberg L-functions for GL(n) x GL(m), where n + m = N. The authors carry through the entire program with an eye toward generalizations.This book should be of interest to advanced graduate students and researchers interested in number theory, automorphic forms, representation theory, and the cohomology of arithmetic groups.

Produkt-Details

• Erscheint lt. Verlag: 3.12.2019
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 1 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Addition • Adele ring • algebraic group • algebraic number theory • arithmetic group • Automorphic form • Base change • Basis (linear algebra) • Bearing (navigation) • Borel subgroup • Calculation • category of groups • coefficient • cohomology • combination • Commutative Ring • Compact Group • Computation • conjecture • Constant term • corollary • Covering space • Critical Value • Diagram (category theory) • Dimension • Dirichlet character • Discrete series representation • discrete spectrum • Eigenvalues and Eigenvectors • Eisenstein series • Elaboration • Embedding • Euler product • Field Extension • Field of fractions • Free module • Freydoon Shahidi • Function field • functor • Galois group • Ground field • Group (mathematics) • group scheme • Harish-Chandra • Hecke character • Hecke L-function • Hecke Operator • Hereditary property • induced representation • irreducible representation • K0 • Langlands dual group • Level structure • L-Function • Lie algebra • Lie algebra cohomology • Lie group • Linear combination • Linear map • Local System • maximal torus • modular form • Modular symbol • Module (mathematics) • Monograph • N0 • National Science Foundation • Natural number • Natural transformation • Nilradical • Number Theory • Permutation • Prime number • Quantity • Rational number • reductive group • Requirement • Ring of integers • Root of unity • Scalar (physics) • Sheaf (mathematics) • SL2(R) • Special case • Spectral Sequence • Standard L-function • SUBGROUP • Subset • Summation • tensor product • Theorem • theory • Triangular Matrix • Triviality (mathematics) • two-dimensional space • Unitary Group • Vector Space • W0 • Weyl Group
• ISBN-10: 0-691-19793-8 / 0691197938
• ISBN-13: 978-0-691-19793-7 / 9780691197937