L 2 -cohomology and intersection homology of locally symmetric varieties, II

Steven Zucker

Compositio Mathematica (1986)

  • Volume: 59, Issue: 3, page 339-398
  • ISSN: 0010-437X

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Zucker, Steven. "$L_2$-cohomology and intersection homology of locally symmetric varieties, II." Compositio Mathematica 59.3 (1986): 339-398. <http://eudml.org/doc/89791>.

@article{Zucker1986,
author = {Zucker, Steven},
journal = {Compositio Mathematica},
keywords = {Baily-Borel-Satake compactification; middle perversity intersection homology; -cohomology},
language = {eng},
number = {3},
pages = {339-398},
publisher = {Martinus Nijhoff Publishers},
title = {$L_2$-cohomology and intersection homology of locally symmetric varieties, II},
url = {http://eudml.org/doc/89791},
volume = {59},
year = {1986},
}

TY - JOUR
AU - Zucker, Steven
TI - $L_2$-cohomology and intersection homology of locally symmetric varieties, II
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 59
IS - 3
SP - 339
EP - 398
LA - eng
KW - Baily-Borel-Satake compactification; middle perversity intersection homology; -cohomology
UR - http://eudml.org/doc/89791
ER -

References

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  1. [1] W. Baily and A. Borel: Compactifications of arithmetic quotients of bounded symmetric domains. Ann. of Math.84 (1966) 442-528. Zbl0154.08602MR216035
  2. [2] A. Borel: Introduction aux Groupes Arithmétiques. Paris: Hermann (1969). Zbl0186.33202MR244260
  3. [3] A. Borel: Stable real cohomology of arithmetic groups. Ann. Sci. ENS7 (1974) 235-272. Zbl0316.57026MR387496
  4. [4] A. Borel: L2-cohomology and intersection cohomology of certain arithmetic varieties Emmy Noether in Bryn Mawr. Berlin- Heidelberg-New York: Springer-Verlag (1983) 119-131. Zbl0541.14015MR713796
  5. [5] A. Borel and J.-P. Serre: Corners and arithmetic groups. Commentarii Math. Helv.48 (1973) 436-491. Zbl0274.22011MR387495
  6. [6] A. Borel and J. Tits: Groupes réductifs. Pub. Math. IHES27 (1965) 55-151. Zbl0145.17402MR207712
  7. [7] N. Bourbaki: Groupes et Algèbres de Lie. Eléments de MathématiquesXXXIV. Paris: Hermann (1968). Zbl0213.04103MR240238
  8. [8] J.-L. Brylinski and J.-P. Labesse: Cohomologie d'intersection et fonctions L de certaines variétés de Shimura. Ann. Sci. ENS17 (1984) 361-412. Zbl0553.12005MR777375
  9. [9] J. Cheeger: On the Hodge theory of Riemannian pseudomanifolds. Proc. Symposia Pure Math.36 (1980) 91-146. Providence: AMS. Zbl0461.58002MR573430
  10. [10] M. Goresky and R. Macpherson: Intersection homology, II. Inventiones Math.72 (1983) 77-129. Zbl0529.55007MR696691
  11. [11] S. Helgason: Differential Geometry, Lie Groups, and Symmetric Spaces. New York-San Francisco-London: Academic Press (1978). Zbl0451.53038MR514561
  12. [12] J. Humphreys: Introduction to Lie Algebras. Berlin-Heidelberg-New York: Springer-Verlag (1972). Zbl0254.17004MR323842
  13. [13] M. Rosenlicht: Some basic theorems on algebraic groups. Amer. J. Math.78 (1956) 401-443. Zbl0073.37601MR82183
  14. [14] G. Warner: Harmonic Analysis on Semi-Simple Lie Groups I. Berlin- Heidelberg-New York: Springer-Verlag (1972). Zbl0265.22020MR498999
  15. [15] S. Zucker: L2 cohomology of warped products and arithmetic groups. Inventiones Math.70 (1982) 169-218. Zbl0508.20020MR684171
  16. [16] S. Zucker: L2-cohomology and intersection homology of locally symmetric varieties. Proc. Symposia Pure Math.40, Part 2 (1983) 675-680. Providence: AMS. Zbl0545.55005
  17. [17] S. Zucker: Satake compactifications. Commentarii Math. Helv.58 (1983) 312-343. Zbl0565.22009MR705539
  18. [18] A. Borel and W. Casselman: L2-cohomology of locally symmetric manifolds of finite volume. Duke Math. J.50 (1983) 625-647. Zbl0528.22012MR714821
  19. [19] J. Tits: Classification of algebraic semisimple groups. Proc. Symposia Pure Math.9 (1966) 33-62. Providence: AMS. Zbl0238.20052MR224710
  20. [20] D. Vogan and G. Zuckerman: Unitary representations with non-zero cohomology. Comp. Math.53 (1984) 51-90. Zbl0692.22008MR762307
  21. [21] A. Borel and W. Casselman: Cohomologie d'intersection et L2-cohomologie de variétés arithmétiques de rang rationnel 2. C.R. Acad. Sc. Paris301 (1985) 369-373. Zbl0612.14018MR808630
  22. [22] W. Casselman: Introduction to the L2-cohomology of arithmetic quotients of bounded symmetric domains, 1985. Zbl0669.22004

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