02182nam a2200229 450000500170000000800410001702000180005804000150007604100080009108200180009910000210011724501210013826000490025930000130030844000440032152013770036565000180174270000170176094200070177799900190178495201490180320200306123324.0200304b xxu||||| |||| 00| 0 eng d a9780691197883 cIIT Kanpur aeng a514.23bH218e aHarder, Günter aEisenstein cohomology for GLn and the special values of rankin-selberg L-functions cGünter Harder and A. Raghuram aPrinceton bPrinceton University Pressc2020 axi, 220p aAnnals of mathematics studies ; no. 203 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.
aNumber theory aRaghuram, A. cBK c561472d561472 0010406514_230000000000000_H218E708COMPACT ST9901662aIITKbIITKd2020-03-16l3o514.23 H218epGB1842r2020-09-03s2020-09-03v12667.00yBK