Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting

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  • Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting Book Detail

  • Author : J. P. Pridham
  • Release Date : 2016-09-06
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 190
  • ISBN 13 : 1470419815
  • File Size : 50,50 MB
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Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting by J. P. Pridham PDF Summary

Book 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 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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Rationality Problem for Algebraic Tori

Rationality Problem for Algebraic Tori

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The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classificatio