000			02024nam a2200217 4500
005			20200306123324.0
008			200304b xxu||||| |||| 00| 0 eng d
020			_a9780691197883
040			_cIIT Kanpur
041			_aeng
082			_a514.23 _bH218e
100			_aHarder, Günter
245			_aEisenstein cohomology for GLn and the special values of rankin-selberg L-functions _cGünter Harder and A. Raghuram
260			_aPrinceton _bPrinceton University Press _c2020
300			_axi, 220p
440			_aAnnals of mathematics studies ; no. 203
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			_aNumber theory
700			_aRaghuram, A.
942			_cBK
999			_c561472 _d561472