The intersection cohomology of the Satake compactification of $${\mathcal {A}}_g$$Ag for $$g \le 4$$g≤4
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DOI: 10.1007/s00208-016-1491-1
Abstract: We completely determine the intersection cohomology of the Satake compactifications $${{\mathcal {A}}_{2}^{\mathrm{Sat}}},{{\mathcal {A}}_{3}^{\mathrm{Sat}}}$$A2Sat,A3Sat, and $${{\mathcal {A}}_{4}^{\mathrm{Sat}}}$$A4Sat, except for $${ IH}^{10}({{\mathcal {A}}_{4}^{\mathrm{Sat}}})$$IH10(A4Sat). We also determine all the ingredients appearing in the decomposition theorem applied to the… read more here.
Keywords: compactification; mathcal mathrm; mathrm sat; cohomology ... See more keywords
On q-de Rham cohomology via $$\Lambda $$Λ-rings
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DOI: 10.1007/s00208-019-01806-7
Abstract: We show that Aomoto’s q-deformation of de Rham cohomology arises as a natural cohomology theory for $$\Lambda $$Λ-rings. Moreover, Scholze’s $$(q-1)$$(q-1)-adic completion of q-de Rham cohomology depends only on the Adams operations at each residue… read more here.
Keywords: rham cohomology; via lambda; cohomology; lambda rings ... See more keywords
Rigid cohomology of Drinfeld’s upper half space over a finite field
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DOI: 10.1007/s00209-017-1951-7
Abstract: In this paper the rigid cohomology of Drinfeld’s upper half space over a finite field is computed in two ways. The first method proceeds by computation of the rigid cohomology of the complement of Drinfeld’s… read more here.
Keywords: space; cohomology; half space; upper half ... See more keywords
Computations in $$C_{pq}$$Cpq-Bredon cohomology
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DOI: 10.1007/s00209-019-02248-2
Abstract: In this paper, we compute the $$RO(C_{pq})$$RO(Cpq)-graded cohomology of $$C_{pq}$$Cpq-orbits. We deduce that in all the cases the Bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations. Further,… read more here.
Keywords: computations cpq; cpq bredon; cohomology; bredon cohomology ... See more keywords
Classification of Quantum Groups via Galois Cohomology
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DOI: 10.1007/s00220-019-03597-z
Abstract: The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called $$U_q (\mathfrak {sl}(2))$$… read more here.
Keywords: quantum; quantum groups; galois cohomology; cohomology ... See more keywords
Cohomology of Fuchsian groups and non-Euclidean crystallographic groups
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DOI: 10.1007/s00229-022-01369-z
Abstract: For each geometrically finite 2-dimensional non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology. read more here.
Keywords: group; cohomology fuchsian; euclidean crystallographic; cohomology ... See more keywords
The $${\mathcal {L}}_B$$LB-cohomology on compact torsion-free $$\mathrm {G}_2$$G2 manifolds and an application to ‘almost’ formality
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DOI: 10.1007/s10455-018-9629-x
Abstract: We study a cohomology theory $$H^{\bullet }_{\varphi }$$Hφ∙, which we call the $${\mathcal {L}}_B$$LB-cohomology, on compact torsion-free $$\mathrm {G}_2$$G2 manifolds. We show that $$H^k_{\varphi } \cong H^k_{\mathrm {dR}}$$Hφk≅HdRk for $$k \ne 3, 4$$k≠3,4, but that $$H^k_{\varphi… read more here.
Keywords: torsion free; compact torsion; cohomology; mathrm ... See more keywords
The Second Cohomology Spaces $$ \mathcal{K} $$(2) with Coefficients in the Superspace of Weighted Densities
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DOI: 10.1007/s11253-021-01870-w
Abstract: Over the (1, 2)-dimensional supercircle, we investigate the second cohomology space associated with the Lie superalgebra $$ \mathcal{K} $$ (2) of vector fields on the supercircle S1|2 with coefficients in the space of weighted densities.… read more here.
Keywords: cohomology; weighted densities; mathcal coefficients; second cohomology ... See more keywords
Classical and variational Poisson cohomology
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DOI: 10.1007/s11537-021-2109-2
Abstract: We prove that, for a Poisson vertex algebra V, the canonical injective homomorphism of the variational cohomology of V to its classical cohomology is an isomorphism, provided that V, viewed as a differential algebra, is… read more here.
Keywords: poisson cohomology; cohomology classical; cohomology; poisson ... See more keywords
Extensions and Deformations of Algebras with Higher Derivations
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DOI: 10.1007/s40840-021-01197-6
Abstract: Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs… read more here.
Keywords: algebras higher; extensions deformations; cohomology; higher derivations ... See more keywords
Modular characteristic classes for representations over finite fields
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DOI: 10.1016/j.aim.2017.10.029
Abstract: Abstract The cohomology of the degree-n general linear group over a finite field of characteristic p, with coefficients also in characteristic p, remains poorly understood. For example, the lowest degree previously known to contain nontrivial… read more here.
Keywords: nontrivial elements; characteristic classes; finite fields; cohomology ... See more keywords