Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Globally Analytic p-adic Representations of the Pro–p Iwahori Subgroup of GL(2) and Base Change, II: A Steinberg Tensor Product Theorem Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Eisenstein Cohomology and Automorphic L-Functions

verfasst von : Neven Grbac

Erschienen in: Cohomology of Arithmetic Groups

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

During the past ten years of the most inspiring and very fruitful collaboration with Joachim Schwermer, we have carefully studied the non-vanishing conditions for certain summands in the decomposition along the cuspidal support of the (square-integrable) Eisenstein cohomology of a reductive group over a totally real number field. These conditions form a subtle combination of geometric conditions, arising from cohomological considerations, and arithmetic conditions, arising from the analytic properties of Eisenstein series and given in terms of automorphic L-functions. This paper is a survey of the most important results of our long-lasting collaboration.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Globally Analytic p-adic Representations of the Pro–p Iwahori Subgroup of GL(2) and Base Change, II: A Steinberg Tensor Product Theorem
Nächstes Kapitel Eisenstein Cohomology for and Special Values of L-Functions
Literatur
1.
Li, J.-S., Schwermer, J.: Automorphic representations and cohomology of arithmetic groups. In: Challenges for the 21st century (Singapore, 2000), pp. 102–137. World Scientific Publishing, River Edge, NJ (2001)
2.
Schwermer, J.: The cohomological approach to cuspidal automorphic representations. Automorphic Forms and \(L\)-Functions I. Global Aspects. Contemporary Mathematics, vol. 488, pp. 257–285. American Mathematical Society, Providence (2009)
3.
Schwermer, J.: Geometric cycles, arithmetic groups and their cohomology. Bull. Am. Math. Soc. (N.S.) 47(2), 187–279 (2010)MathSciNetCrossRef
4.
Mœglin, C., Waldspurger, J.-L.: Spectral Decomposition and Eisenstein Series, Cambridge Tracts in Mathematics, vol. 113. Cambridge University Press, Cambridge (1995)
5.
Borel, A., Jacquet, H.: Automorphic Forms and Automorphic Representations. In: Automorphic forms, representations and \(L\)-functions, Proceedings of Symposia Pure Mathematics, XXXIII, Part 1, pp. 189–202. American Mathematical Society, Providence (1979)
6.
Borel, A.: Regularization theorems in Lie algebra cohomology. Applications. Duke Math. J. 50(3), 605–623 (1983)MathSciNetCrossRef
7.
Borel, A., Wallach, N.: Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. Mathematical Surveys and Monographs, vol. 67, 2nd edn. American Mathematical Society, Providence (2000)
8.
Franke, J.: Harmonic analysis in weighted \(L_2\)-spaces. Ann. Sci. École Norm. Super. (4) 31(2), 181–279 (1998)
9.
Franke, J., Schwermer, J.: A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups. Math. Ann. 311(4), 765–790 (1998)MathSciNetCrossRef
10.
Langlands, R.P.: On the Functional Equations Satisfied by Eisenstein Series. Lecture Notes in Mathematics, vol. 544. Springer, Berlin (1976)CrossRef
11.
Li, J.-S., Schwermer, J.: On the Eisenstein cohomology of arithmetic groups. Duke Math. J. 123(1), 141–169 (2004)MathSciNetCrossRef
12.
Schwermer, J.: Kohomologie Arithmetisch Definierter Gruppen und Eisensteinreihen. Lecture Notes in Mathematics, vol. 988. Springer, Berlin (1983)CrossRef
13.
Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math. 74(2), 329–387 (1961)MathSciNetCrossRef
14.
Borel, A., Casselman, W.: \(L_{2}\)-cohomology of locally symmetric manifolds of finite volume. Duke Math. J. 50(3), 625–647 (1983)MathSciNetCrossRef
15.
Vogan Jr., D.A., Zuckerman, G.J.: Unitary representations with nonzero cohomology. Compos. Math. 53(1), 51–90 (1984)
16.
Grbac, N., Schwermer, J.: On Eisenstein series and the cohomology of arithmetic groups. C. R. Math. Acad. Sci. Paris 348(11–12), 597–600 (2010)
17.
Grbac, N., Schwermer, J.: Eisenstein series, cohomology of arithmetic groups, and automorphic \(L\)-functions at half integral arguments. Forum Math. 26(6), 1635–1662 (2014)
18.
Grbac, N., Schwermer, J.: Eisenstein cohomology for unitary groups I. The case of relative rank one, in preparation
19.
Shahidi, F.: A proof of Langlands’ conjecture on Plancherel measures; complementary series for \(p\)-adic groups. Ann. Math. (2) 132(2), 273–330 (1990)
20.
Shahidi, F.: Eisenstein Series and Automorphic \(L\)-Functions. American Mathematical Society Colloquium Publications, vol. 58. American Mathematical Society, Providence (2010)
21.
Cogdell, J.W., Kim, H.H., Piatetski-Shapiro, I.I., Shahidi, F.: On lifting from classical groups to \(GL_N\). Publ. Math. Inst. Hautes Études Sci. 93, 5–30 (2001)
22.
Cogdell, J.W., Kim, H.H., Piatetski-Shapiro, I.I., Shahidi, F.: Functoriality for the classical groups. Publ. Math. Inst. Hautes Études Sci. 99, 163–233 (2004)MathSciNetCrossRef
23.
Grbac, N.: On the residual spectrum of split classical groups supported in the Siegel maximal parabolic subgroup. Monatsh. Math. 163(3), 301–314 (2011)MathSciNetCrossRef
24.
Grbac, N., Shahidi, F.: Endoscopic transfer for unitary groups and holomorphy of Asai \(L\)-functions. Pac. J. Math. 276(1), 185–211 (2015)
25.
Arthur, J.: The Endoscopic Classification of Representations. American Mathematical Society Colloquium Publications, vol. 61. American Mathematical Society, Providence (2013)
26.
Grbac, N., Schwermer, J.: On residual cohomology classes attached to relative rank one Eisenstein series for the symplectic group. Int. Math. Res. Not. IMRN (7), 1654–1705 (2011)
27.
Gotsbacher, G., Grobner, H.: On the Eisenstein cohomology of odd orthogonal groups. Forum Math. 25(2), 283–311 (2013)
28.
Trotabas, D.: Non annulation des fonctions \(L\) des formes modulaires de Hilbert au point central. Ann. Inst. Fourier (Grenoble) 61(1), 187–259 (2011)MathSciNetCrossRef
29.
Grbac, N., Schwermer, J.: A non-vanishing result for the residual Eisenstein cohomology of arithmetic groups of low rank (preprint)
30.
Rohlfs, J., Speh, B.: Pseudo Eisenstein forms and the cohomology of arithmetic groups III: residual cohomology classes. On Certain \(L\)-Functions. Clay Mathematics Proceedings, vol. 13, pp. 501–523. American Mathematical Society, Providence (2011)
31.
Grbac, N.: The Franke filtration of the spaces of automorphic forms supported in a maximal proper parabolic subgroup. Glas. Mat. Ser. III. 47(67)(2), 351–372 (2012)MathSciNetCrossRef
32.
Grbac, N., Grobner, H.: The residual Eisenstein cohomology of \(Sp_4\) over a totally real number field. Trans. Am. Math. Soc. 365(10), 5199–5235 (2013)MathSciNetCrossRef
33.
Schwermer, J.: On arithmetic quotients of the Siegel upper half space of degree two. Compos. Math. 58(2), 233–258 (1986)
34.
Grobner, H.: Residues of Eisenstein series and the automorphic cohomology of reductive groups. Compos. Math. 149, 1061–1090 (2013)MathSciNetCrossRef
Metadaten
Titel
Eisenstein Cohomology and Automorphic L-Functions
verfasst von
Neven Grbac
Copyright-Jahr
2018
Buch
Cohomology of Arithmetic Groups

Print ISBN: 978-3-319-95548-3

Electronic ISBN: 978-3-319-95549-0

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-95549-0_2