Cohomology groups

On the Cohomology Groups of Moduli Spaces of Vector Bundles on Curves, Math. Ann. 212 (1975), 215-248. 

This lemma is equivalent to saying that X/G is a rational homology manifold. It holds because we have the Poincare duality isomorphism for the cohomology groups with rational coefficients on X/G. 

Consider the top degree cohomology group i/ dmiTr of the fiber ir y),... 

They are dehned by identifying locally hnite homology groups with relative cohomology groups. For example, the lower homomorphism is induced from... 

Oda, T. The First De Rham Cohomology Group and Dieudonne Modules, Ann. Sci. Ecole Norm. Sup., 1969-... 

Finally we remark that, from the functor p above, we get homomorphisms of the cohomology groups (in case E is a H-group)t... 

This gives an exact sequence of cohomology groups ... 

With the usual interplay between profinite groups and projective systems of sheaves for the tale topology on Uq we have the following commutative diagram (see 5 2.8 by abuse of language we also use the letter j for the induced maps of the cohomology groups) ... 

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