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 equipped wit...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pridham, J. P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2016.
Colección:Memoirs of the American Mathematical Society.
Temas:
Hodge theory.
Homology theory.
Théorie de Hodge.
Homologie.
Hodge theory
Homology theory
Acceso en línea:Texto completo

MARC

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049 |a UAMI 
100 1 |a Pridham, J. P. 
245 1 0 |a Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties. 
260 |a Providence :  |b American Mathematical Society,  |c 2016. 
300 |a 1 online resource (190 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Memoirs of the American Mathematical Society ;  |v v. 243 
588 0 |a Print version record. 
505 0 |a Cover; Title page; Introduction; Structure of the paper; Notation; Chapter 1. Splittings for MHS on real homotopy types; 1.1. The family of formality quasi-isomorphisms; 1.2. The reduced bar construction; 1.3. The mixed Hodge structure on Quillen's real homotopy type and on homotopy groups; Chapter 2. Non-abelian structures; 2.1. Hodge filtrations; 2.2. Twistor filtrations; 2.3. Mixed Hodge structures; 2.4. Mixed twistor structures; 2.5. Real homotopy types revisited; Chapter 3. Structures on cohomology; 3.1. Cohomology of Hodge filtrations; 3.2. Cohomology of MHS. 
505 8 |a 3.3. Real Deligne cohomology; 3.4. Analogies with limit Hodge structures; 3.5. Archimedean cohomology; Chapter 4. Relative Malcev homotopy types; 4.1. Review of pro-algebraic homotopy types; 4.2. Cosimplicial and DG Hopf algebras; 4.3. Equivalent formulations; 4.4. The reduced bar construction; 4.5. Equivalences of homotopy categories; 4.6. Families of homotopy types; Chapter 5. Structures on relative Malcev homotopy types; 5.1. Homotopy types; 5.2. Grouplike structures; 5.3. Splittings over \cS; 5.4. Mixed Hodge structures on homotopy groups. 
505 8 |a Chapter 6. MHS on relative Malcev homotopy types of compact Kähler manifolds; 6.1. Real homotopy types; 6.2. Relative Malcev homotopy types; Chapter 7. MTS on relative Malcev homotopy types of compact Kähler manifolds; 7.1. Unitary actions; Chapter 8. Variations of mixed Hodge and mixed twistor structures; 8.1. Representations in MHS/MTS; 8.2. Enriching VMTS; 8.3. Absolute Hodge and twistor homotopy types; Chapter 9. Monodromy at the Archimedean place; 9.1. Reformulation via _{∞} derivations; 9.2. Kähler identities; 9.3. Monodromy calculation; Chapter 10. Simplicial and singular varieties 
505 8 |a 10.1. Semisimple local systems; 10.2. The Malcev homotopy type; 10.3. Mixed Hodge structures; 10.4. Enriching twistor structures; Chapter 11. Algebraic MHS/MTS for quasi-projective varieties I; 11.1. The Hodge and twistor filtrations; 11.2. Higher direct images and residues; 11.3. Opposedness; 11.4. Singular and simplicial varieties; Chapter 12. Algebraic MHS/MTS for quasi-projective varieties II -non-trivial monodromy; 12.1. Constructing mixed Hodge structures; 12.2. Constructing mixed twistor structures; 12.3. Unitary monodromy; 12.4. Singular and simplicial varieties. 
505 8 |a 12.5. More general monodromy; Chapter 13. Canonical splittings; 13.1. Splittings of mixed Hodge structures; 13.2. Splittings of mixed twistor structures; 13.3. Reduced forms for Hodge and twistor homotopy types; Chapter 14. \SL₂ splittings of non-abelian MTS/MHS and strictification; 14.1. Simplicial structures; 14.2. Functors parametrising Hodge and twistor structures; 14.3. Deformations; 14.4. Quasi-projective varieties; Bibliography; Back Cover. 
520 |a 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 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. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Hodge theory. 
650 0 |a Homology theory. 
650 4 |a Hodge theory. 
650 6 |a Théorie de Hodge. 
650 6 |a Homologie. 
650 7 |a Hodge theory  |2 fast 
650 7 |a Homology theory  |2 fast 
758 |i has work:  |a Real non-abelian mixed Hodge structures for quasi-projective varieties (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGWhFBjWbgXyx7r6mrR64y  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Pridham, J.P.  |t Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting.  |d Providence : American Mathematical Society, ©2016  |z 9781470419813 
830 0 |a Memoirs of the American Mathematical Society. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4901869  |z Texto completo 
938 |a EBL - Ebook Library  |b EBLB  |n EBL4901869 
994 |a 92  |b IZTAP 

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