Vanishing on cohomology associated to Hermitian symmetric spaces

DOI10.5802/aif.1119zbMath0625.57023OpenAlexW2047903257MaRDI QIDQ579688

Shingo Murakami

Publication date: 1987

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1987__37_4_225_0

zbMATH Keywords

canonical automorphic factorscoefficients in the sheaf of germs of holomorphic sectionscohomology groups of compact locally Hermitian symmetric spaces

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Homology and cohomology of homogeneous spaces of Lie groups (57T15)

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Cites Work

• Vanishing theorems for type (0,q) cohomology of locally symmetric spaces. II
• Theta functions and holomorphic differential forms on compact quotients of bounded symmetric domains
• Locally homogeneous variations of Hodge structure
• Criteria for the unitarizability of some highest weight modules
• On the canonical \(k\)-types in the irreducible unitary \(\mathfrak g\)-modules with non-zero relative cohomology
• Vanishing theorems for type (0,q) cohomology of locally symmetric spaces
• Certain cohomology groups attached to Hermitian symmetric spaces and unitary representations
• On Matsushima's formula for the Betti numbers of a locally symmetric space
• On a vanishing theorem for certain cohomology groups
• On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds
• On certain cohomology groups attached to Hermitian symmetric spaces
• A formula for the Betti numbers of compact locally symmetric Riemannian manifolds
• On certain cohomology groups attached to Hermitian symmetric spaces. II
• A note on the vanishing of certain \(L^ 2\)-cohomologies
• On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces
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