Real non-Abelian mixed Hodge structures for quasi-projective varieties : formality and splitting
著者
書誌事項
Real non-Abelian mixed Hodge structures for quasi-projective varieties : formality and splitting
（Memoirs of the American Mathematical Society, no. 1150）
American Mathematical Society, c2016
大学図書館所蔵 全9件
注記
Includes bibliographical references
"Volume 243, number 1150 (third of 4 numbers), September 2016"
内容説明・目次
内容説明
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.
目次
Introduction
Splittings for MHS on real homotopy types
Non-abelian structures
Structures on cohomology
Relative Malcev homotopy types
Structures on relative Malcev homotopy types
MHS on relative Malcev homotopy types of compact Kahler manifolds
MTS on relative Malcev homotopy types of compact Kahler manifolds
Variations of mixed Hodge and mixed twistor structures
Monodromy at the Archimedean place
Simplicial and singular varieties
Algebraic MHS/MTS for quasi-projective varieties I
Algebraic MHS/MTS for quasi-projective varieties II - non-trivial monodromy
Canonical splittings
${\rm SL}_2$ splittings of non-abelian MTS/MHS and strictification
Bibliography.
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