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Relative Cohomology and Generalized Tate Cohomology
Algebras and Representation Theory, 2017Let \(R\) be a ring with identity, all \(R\)-modules in the paper are considered to be left modules and unitary. Using proper resolutions of modules over \(R\), the authors of this paper discuss relative homological dimensions and relative derived functors.
Bin Yu, Xiaosheng Zhu, Yanbo Zhou
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Coarse Cohomology and lp-Cohomology
K-Theory, 1998Let \(G\) be a connected, undirected infinite graph with uniformly bounded vertex degrees. For any \(k\in\mathbb{N}\) and \(k=\infty\) the \(k\)th reduced and unreduced \(\ell_p\)-cohomologies for those graphs are defined: \(HX^k_{(p)}(G)\) and \(\overline{HX}^k_{(p)}(G)\).
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Canadian Journal of Mathematics, 1957
It is our purpose in this paper to present certain aspects of a cohomology theory of a ring R relative to a subring S, basing the theory on the notions of induced and produced pairs of our earlier paper (2), but making the paper self-contained except for ...
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It is our purpose in this paper to present certain aspects of a cohomology theory of a ring R relative to a subring S, basing the theory on the notions of induced and produced pairs of our earlier paper (2), but making the paper self-contained except for ...
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Publicationes Mathematicae Debrecen, 2005
Let \(S\) be a monoid and \(A\) a right \(S\)-set. A right \(S\)-set over \(A\) is a pair of a right \(S\)-set \(X\) and a homomorphism of \(S\)-sets \(\xi\colon X\to A\); \(\overline{\mathbf C}\) is the category of all right \(S\)-sets over \(A\) and their homomorphisms.
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Let \(S\) be a monoid and \(A\) a right \(S\)-set. A right \(S\)-set over \(A\) is a pair of a right \(S\)-set \(X\) and a homomorphism of \(S\)-sets \(\xi\colon X\to A\); \(\overline{\mathbf C}\) is the category of all right \(S\)-sets over \(A\) and their homomorphisms.
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2007
Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields.
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Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields.
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Formal Cohomology: II. The Cohomology Sequence of a Pair
The Annals of Mathematics, 1968Now Grothendieck has shown that the cohomology of a complex variety may be defined algebraically; in particular if X is a complex affine variety the canonical map from the closed/exact algebraic differentials on X to the DeRham cohomology of X is bijective.
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Continuous cohomology and differentiable cohomology
2000A. Borel, N. Wallach
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Dirac cohomology and u-cohomology
2002We exhibit the relationship between Dirac cohomology of a Harish-Chandra module and its u-cohomology with respect to he nilradical of a theta-stable parabolic subalgebra in certain special cases.
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