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Fuetaro Yobuko - One of the best experts on this subject based on the ideXlab platform.
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degenerations of log hodge de rham spectral sequences log kodaira vanishing theorem in characteristic p 0 and log weak lefschetz conjecture for log crystalline Cohomologies
European Journal of Mathematics, 2021Co-Authors: Yukiyoshi Nakkajima, Fuetaro YobukoAbstract:We prove that the log Hodge de Rham spectral sequences of certain proper log smooth schemes of Cartier type in characteristic $$p>0$$ degenerate at $$E_1$$ . We also prove that the log Kodaira vanishings for them hold when they are projective. We formulate the log weak Lefschetz conjecture for log crystalline Cohomologies and prove that it is true in certain cases.
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degenerations of log hodge de rham spectral sequences log kodaira vanishing theorem in characteristic p 0 and log weak lefschetz conjecture for log crystalline Cohomologies
arXiv: Algebraic Geometry, 2019Co-Authors: Yukiyoshi Nakkajima, Fuetaro YobukoAbstract:In this article we prove that the log Hodge de Rham spectral sequences of certain proper log smooth schemes of Cartier type in characteristic $p>0$ degenerate at $E_1$. We also prove that the log Kodaira vanishings for them hold when they are projective. We formulate the log weak Lefschetz conjecture for log crystalline Cohomologies and prove that it is true in certain cases.
Luis Ugarte - One of the best experts on this subject based on the ideXlab platform.
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higher page bott chern and aeppli Cohomologies and applications
Crelle's Journal, 2021Co-Authors: Dan Popovici, Jonas Stelzig, Luis UgarteAbstract:For every positive integer $r$, we introduce two new Cohomologies, that we call $E_r$-Bott-Chern and $E_r$-Aeppli, on compact complex manifolds. When $r=1$, they coincide with the usual Bott-Chern and Aeppli Cohomologies, but they are coarser, respectively finer, than these when $r\geq 2$. They provide analogues in the Bott-Chern-Aeppli context of the $E_r$-Cohomologies featuring in the Frolicher spectral sequence of the manifold. We apply these new Cohomologies in several ways to characterise the notion of page-$(r-1)$-$\partial\bar\partial$-manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott-Chern and Aeppli Cohomologies and for the spaces featuring in the Frolicher spectral sequence. We obtain a further group of applications of our Cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.
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symplectic harmonicity and generalized coeffective Cohomologies
Annali di Matematica Pura ed Applicata, 2019Co-Authors: Luis Ugarte, Raquel VillacampaAbstract:Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective version of the filtered Cohomologies introduced by Tsai, Tseng and Yau. We construct closed (simply connected) manifolds endowed with a family of symplectic forms \(\omega _t\) such that the dimensions of these symplectic cohomology groups vary with respect to t. A complete study of these Cohomologies is given for 6-dimensional symplectic nilmanifolds, and concrete examples with special cohomological properties are obtained on an 8-dimensional solvmanifold and on 2-step nilmanifolds in higher dimensions.
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the dδ lemma for weakly lefschetz symplectic manifold
2005Co-Authors: Marisa Fernandez, Vicente Muñoz, Luis UgarteAbstract:For a symplectic manifold (M, ω), not necessarily hard Lefschetz, we prove a version of the Merkulov dδ–lemma ([17, 4]). We also study the dδ–lemma and related Cohomologies for compact symplectic solvmanifolds.
Yukiyoshi Nakkajima - One of the best experts on this subject based on the ideXlab platform.
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degenerations of log hodge de rham spectral sequences log kodaira vanishing theorem in characteristic p 0 and log weak lefschetz conjecture for log crystalline Cohomologies
European Journal of Mathematics, 2021Co-Authors: Yukiyoshi Nakkajima, Fuetaro YobukoAbstract:We prove that the log Hodge de Rham spectral sequences of certain proper log smooth schemes of Cartier type in characteristic $$p>0$$ degenerate at $$E_1$$ . We also prove that the log Kodaira vanishings for them hold when they are projective. We formulate the log weak Lefschetz conjecture for log crystalline Cohomologies and prove that it is true in certain cases.
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degenerations of log hodge de rham spectral sequences log kodaira vanishing theorem in characteristic p 0 and log weak lefschetz conjecture for log crystalline Cohomologies
arXiv: Algebraic Geometry, 2019Co-Authors: Yukiyoshi Nakkajima, Fuetaro YobukoAbstract:In this article we prove that the log Hodge de Rham spectral sequences of certain proper log smooth schemes of Cartier type in characteristic $p>0$ degenerate at $E_1$. We also prove that the log Kodaira vanishings for them hold when they are projective. We formulate the log weak Lefschetz conjecture for log crystalline Cohomologies and prove that it is true in certain cases.
Rachel Taillefer - One of the best experts on this subject based on the ideXlab platform.
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injective hopf bimodules Cohomologies of infinite dimensional hopf algebras and graded commutativity of the yoneda product
Journal of Algebra, 2004Co-Authors: Rachel TailleferAbstract:Abstract We prove that the category of Hopf bimodules over any Hopf algebra has enough injectives, which enables us to extend some results on the unification of Hopf bimodule Cohomologies of [R. Taillefer, PhD thesis, 2001; arXiv preprint math.QA/0005019 ] to the infinite dimensional case. We also prove that the cup-product defined on these Cohomologies is graded-commutative. Unlike the algebra case (see [S. Schwede, J. Reine Angew. Math. 498 (1998) 153–172]), these methods do not give a non-trivial Gerstenhaber algebra structure on the cohomology we consider. We also comment that the other approach to finding such a structure that we know of (see [M. Farinati, A. Solotar, arXiv preprint math.KT/0207243 ]) also gives a trivial Gerstenhaber algebra structure.
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injective hopf bimodules Cohomologies of infinite dimensional hopf algebras and graded commutativity of the yoneda product
arXiv: K-Theory and Homology, 2002Co-Authors: Rachel TailleferAbstract:We prove that the category of Hopf bimodules over any Hopf algebra has enough injectives, which enables us to extend some results on the unification of Hopf bimodule Cohomologies of [T1,T2] to the infinite dimensional case. We also prove that the cup-product defined on these Cohomologies is graded-commutative.
Munoz Bertrand Ruben - One of the best experts on this subject based on the ideXlab platform.
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Coefficients in overconvergent De Rham-Witt cohomology
2020Co-Authors: Munoz Bertrand RubenAbstract:Deligne a défini dans les années 70 le complexe de De Rham-Witt, qui permit à Illusie de prouver un théorème de comparaison avec la cohomologie cristalline. Ce résultat fut ensuite étendu par Etesse aux coefficients. En 2004, Bloch démontra que le théorème de comparaison cohomologique étendu aux coefficients d'Etesse possédait une interprétation plus profonde : sous certaines conditions, on obtient en fait une équivalence de catégories entre des cristaux et des connexions de De Rham Witt.Plus récemment, Davis, Langer et Zink ont introduit un complexe de De Rham-Witt surconvergent et démontré des théorèmes de comparaison avec les Cohomologies de Monsky-Washnitzer et rigide. Ces derniers furent ensuite étendus aux coefficients par Ertl, qui démontra notamment un quasi-isomorphisme de cohomologie avec les isocristaux surconvergents.On peut alors légitimement se demander si les résultats de Bloch possèdent une variante surconvergente : c'est-à-dire que l'on aimerait pouvoir obtenir une interprétation des isocristaux surconvergents pour la cohomologie de De Rham-Witt surconvergente. On peut y parvenir en considérant des connexions de De Rham-Witt surconvergentes comme définies par Ertl, pour lesquelles on peut raisonnablement espérer retrouver les mêmes opérations cohomologiques que pour les F-isocristaux.Cette question fut la motivation de cette thèse, et le théorème principal de ce travail y répond en partie positivement. Pour y parvenir, il est nécessaire d'expliciter la structure locale du complexe de De Rham-Witt surconvergent, et de redéfinir la notion de surconvergence afin de pouvoir mieux contrôler la convergence des produits de différentielles de De Rham-Witt.Under a few assumptions, we prove an equivalence of category between a subcategory of F-isocristals on a smooth algebraic variety and overcongergent integrable De Rham-Witt connections. We do so by giving an equivalent definition of overconvergence, and by studying the explicit local structure of the De Rham-Witt complex
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Coefficients en cohomologie de De Rham-Witt surconvergente
HAL CCSD, 2020Co-Authors: Munoz Bertrand RubenAbstract:Under a few assumptions, we prove an equivalence of category between a subcategory of F-isocristals on a smooth algebraic variety and overcongergent integrable De Rham-Witt connections. We do so by giving an equivalent definition of overconvergence, and by studying the explicit local structure of the De Rham-Witt complex.Deligne a défini dans les années 70 le complexe de De Rham-Witt, qui permit à Illusie de prouver un théorème de comparaison avec la cohomologie cristalline. Ce résultat fut ensuite étendu par Etesse aux coefficients. En 2004, Bloch démontra que le théorème de comparaison cohomologique étendu aux coefficients d'Etesse possédait une interprétation plus profonde : sous certaines conditions, on obtient en fait une équivalence de catégories entre des cristaux et des connexions de De Rham Witt.Plus récemment, Davis, Langer et Zink ont introduit un complexe de De Rham-Witt surconvergent et démontré des théorèmes de comparaison avec les Cohomologies de Monsky-Washnitzer et rigide. Ces derniers furent ensuite étendus aux coefficients par Ertl, qui démontra notamment un quasi-isomorphisme de cohomologie avec les isocristaux surconvergents.On peut alors légitimement se demander si les résultats de Bloch possèdent une variante surconvergente : c'est-à-dire que l'on aimerait pouvoir obtenir une interprétation des isocristaux surconvergents pour la cohomologie de De Rham-Witt surconvergente. On peut y parvenir en considérant des connexions de De Rham-Witt surconvergentes comme définies par Ertl, pour lesquelles on peut raisonnablement espérer retrouver les mêmes opérations cohomologiques que pour les F-isocristaux.Cette question fut la motivation de cette thèse, et le théorème principal de ce travail y répond en partie positivement. Pour y parvenir, il est nécessaire d'expliciter la structure locale du complexe de De Rham-Witt surconvergent, et de redéfinir la notion de surconvergence afin de pouvoir mieux contrôler la convergence des produits de différentielles de De Rham-Witt