Results 171 to 180 of about 17,373 (192)
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Poincar� duality for algebraic de rham cohomology
manuscripta mathematica, 2004This paper provides a careful construction of the de Rham cohomology with compact supports for singular schemes over a field of characteristic zero. The authors prove the algebraic Poincaré duality in this setting.
BALDASSARRI, FRANCESCO +2 more
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2000
The plane ℝ2 and the punctured plane ℝ2 -{(0,0)} are not diffeomorphic, nor even homeomorphic. There are various means by which one can prove this, but the most instructive among these detect the “hole” in the punctured plane (and none in ℝ2) by distinguishing topologically certain “types” of circles that can live in the two spaces.
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The plane ℝ2 and the punctured plane ℝ2 -{(0,0)} are not diffeomorphic, nor even homeomorphic. There are various means by which one can prove this, but the most instructive among these detect the “hole” in the punctured plane (and none in ℝ2) by distinguishing topologically certain “types” of circles that can live in the two spaces.
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Holomorphic de Rham Cohomology
2017We are going to define a natural comparison isomorphism between algebraic de Rham cohomology and singular cohomology of varieties over the complex numbers with coefficients in \(\mathbb {C}\). The link is provided by holomorphic de Rham cohomology, which we study in this chapter.
Annette Huber, Stefan Müller-Stach
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Homology. Cohomology. de Rham Cohomology
1997In mathematics one often encounters the following situation. Let a sequence of abelian groups (modules) ... be given $$ \{ {C^n},n \in \mathbb{Z}\} $$ (1*) together with homomorphisms d n : C n → C n+1 (called differentials or coboundary homomorphisms) for whose $$ {d_{n + 1}}{d_n} = 0 (zero group) for all n. $$ (2*)
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de Rham Cohomology of Local Cohomology Modules
2016Let K be a field of characteristic zero and let \(\mathcal {O}_n\) be the ring \(K[[X_1,\ldots ,X_n]]\). Let \(\mathcal {D}_n = \mathcal {O}_n[\partial _1,\ldots ,\partial _n]\) be the ring of K-linear differential operators on \(\mathcal {O}_n\). Let M be a holonomic \(\mathcal {D}_n\)-module. In this paper we prove \(H^i({\partial }, M) = 0\) for \(i
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De Rham Cohomology of Manifolds
2012In this chapter, we study the topology of C ∞-manifolds. We define the de Rham cohomology of a manifold, which is the vector space of closed differential forms modulo exact forms. After sheafifying the construction, we see that the de Rham complex forms a so-called acyclic resolution of the constant sheaf ℝ.
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2016
In Cartan’s works discussed in the previous chapter, the operations on differential forms were used only for local studies, related to the resolution of Pfaff systems. Only later, in the 1920s, did Cartan get interested in problems concerning the global behaviour of differential forms on manifolds.
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In Cartan’s works discussed in the previous chapter, the operations on differential forms were used only for local studies, related to the resolution of Pfaff systems. Only later, in the 1920s, did Cartan get interested in problems concerning the global behaviour of differential forms on manifolds.
openaire +1 more source