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Real non-abelian mixed hodge structures for quasi-projective varieties

The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring \mathbb{R}[x...

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Autor principal: Pridham, J P
Lenguaje:eng
Publicado: American Mathematical Society 2016
Materias:
Acceso en línea:http://cds.cern.ch/record/2622910
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author Pridham, J P
author_facet Pridham, J P
author_sort Pridham, J P
collection CERN
description The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring \mathbb{R}[x] equipped with the Hodge filtration given by powers of (x-i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2016
publisher American Mathematical Society
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spelling cern-26229102021-04-21T18:48:11Zhttp://cds.cern.ch/record/2622910engPridham, J PReal non-abelian mixed hodge structures for quasi-projective varietiesMathematical Physics and MathematicsThe author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring \mathbb{R}[x] equipped with the Hodge filtration given by powers of (x-i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.American Mathematical Societyoai:cds.cern.ch:26229102016
spellingShingle Mathematical Physics and Mathematics
Pridham, J P
Real non-abelian mixed hodge structures for quasi-projective varieties
title Real non-abelian mixed hodge structures for quasi-projective varieties
title_full Real non-abelian mixed hodge structures for quasi-projective varieties
title_fullStr Real non-abelian mixed hodge structures for quasi-projective varieties
title_full_unstemmed Real non-abelian mixed hodge structures for quasi-projective varieties
title_short Real non-abelian mixed hodge structures for quasi-projective varieties
title_sort real non-abelian mixed hodge structures for quasi-projective varieties
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2622910
work_keys_str_mv AT pridhamjp realnonabelianmixedhodgestructuresforquasiprojectivevarieties