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  1. Bog
  2. Geometri
  3. Algebraisk geometri

Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions

Af: Anantharam Raghuram, Gunter Harder Engelsk Paperback

Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions

Af: Anantharam Raghuram, Gunter Harder Engelsk Paperback
Tjek vores konkurrenters priser

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.

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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.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 240
ISBN-13: 9780691197890
Indbinding: Paperback
Udgave:
ISBN-10: 069119789X
Kategori: Algebraisk geometri
Udg. Dato: 3 dec 2019
Længde: 13mm
Bredde: 162mm
Højde: 238mm
Forlag: Princeton University Press
Oplagsdato: 3 dec 2019
Forfatter(e): Anantharam Raghuram, Gunter Harder
Forfatter(e) Anantharam Raghuram, Gunter Harder

Kategori Algebraisk geometri

ISBN-13 9780691197890

Sprog Engelsk

Indbinding Paperback

Sider 240

Udgave

Længde 13mm

Bredde 162mm

Højde 238mm

Udg. Dato 3 dec 2019

Oplagsdato 3 dec 2019

Forlag Princeton University Press

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