000			02789cam a2200325 i 4500
003			OSt
005			20240511175923.0
008			190923s2019 nju ob 001 0 eng
020			_a9780691197890
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082	0	0	_a515.143.5 _bHAR-E
100	1		_aHarder, Gunter
245	1	0	_aEisenstein cohomology for GLn and the special values of Rankin-Selberg L-functions
260			_aPrinceton : _bPrinceton University Press, _c2020.
300			_axi, 220p.
490			_aAnnals of mathematics studies ; _v203
504			_aIncludes bibliographical references and index.
505			_aIntroduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann.
520			_aThis 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.
650		0	_aShimura varieties..
650		0	_aCohomology operations.
650		0	_aNumber theory
650		0	_aL-FUNCTIONS.
650		0	_aArithmetic groups.
650		0	_aL-functions
700	1		_aRaghuram, A. _q(Anantharam)
856			_3Reviews _uhttps://www.goodreads.com/book/show/45358740-eisenstein-cohomology-for-gln-and-the-special-values-of-rankin-selberg-l?from_search=true&from_srp=true&qid=EHM1y4tWow&rank=2#CommunityReviews
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