FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W57706274> ?p ?o ?g. }

• W57706274 abstract "In the present work, we analyse the categories of mixed Hodge complexes and mixed Hodge diagrams of differential graded algebras in these two directions: we prove the existence of both a Cartan-Eilenberg structure, via the construction of cofibrant minimal models, and a cohomological descent structure. This allows to interpret the results of Deligne, Beilinson, Morgan and Navarro within a common homotopical framework. In the additive context of mixed Hodge complexes we recover Beilinson's results. In our study we go a little further and show that the homotopy category of mixed Hodge complexes, and the derived category of mixed Hodge structures are equivalent to a third category whose objects are graded mixed Hodge structures and whose morphisms are certain homotopy classes, which are easier to manipulate. In particular, we obtain a description of the morphisms in the homotopy category in terms of morphisms and extensions of mixed Hodge structures, and recover the results of Carlson [Car80] in this area. As for the multiplicative analogue, we show that every mixed Hodge diagram can be represented by a mixed Hodge algebra which is Sullivan minimal, and establish a multiplicative version of Beilinson's Theorem. This provides an alternative to Morgan's construction. The main difference between the two approaches is that Morgan uses ad hoc constructions of models a la Sullivan, specially designed for mixed Hodge theory, while we follow the line of Quillen's model categories or Cartan-Eilenberg categories, in which the main results are expressed in terms of equivalences of homotopy categories, and the existence of certain derived functors. In particular, we obtain not only a description of mixed Hodge diagrams in terms of Sullivan minimal algebras, but we also have a description of the morphisms in the homotopy category in terms of certain homotopy classes, parallel to the additive case. In addition, our approach generalizes to broader settings, such as the study of compactificable analytic spaces, for which the Hodge and weight filtrations can be defined, but do not satisfy the properties of mixed Hodge theory. Combining these results with Navarro's functorial construction of mixed Hodge diagrams, and using the cohomological descent structure defined via the Thom-Whitney simple, we obtain a more precise and alternative proof of that the rational homotopy type, and the rational homotopy groups of every simply connected complex algebraic variety inherit functorial mixed Hodge structures. As an application, and extending the Formality Theorem of Deligne-Griffiths-Morgan-Sullivan for compact Kahler varieties and the results of Morgan for open smooth varieties, we prove that every simply connected complex algebraic variety (possibly open and singular) and every morphism between such varieties is filtered formal: its rational homotopy type is entirely determined by the first term of the spectral sequence associated with the multiplicative weight filtration." @default.
• W57706274 created "2016-06-24" @default.
• W57706274 creator A5084737250 @default.
• W57706274 date "2012-06-23" @default.
• W57706274 modified "2023-10-16" @default.
• W57706274 title "Homotopical Aspects of Mixed Hodge Theory" @default.
• W57706274 cites W1493340484 @default.
• W57706274 cites W1511378139 @default.
• W57706274 cites W1515679419 @default.
• W57706274 cites W1518211555 @default.
• W57706274 cites W1530355788 @default.
• W57706274 cites W1538084850 @default.
• W57706274 cites W1539207171 @default.
• W57706274 cites W1541950562 @default.
• W57706274 cites W1543845550 @default.
• W57706274 cites W1551160324 @default.
• W57706274 cites W1587077629 @default.
• W57706274 cites W1599962140 @default.
• W57706274 cites W1981976405 @default.
• W57706274 cites W1984127637 @default.
• W57706274 cites W2005616059 @default.
• W57706274 cites W2008020084 @default.
• W57706274 cites W2009857933 @default.
• W57706274 cites W2018597216 @default.
• W57706274 cites W2025428689 @default.
• W57706274 cites W2027549187 @default.
• W57706274 cites W2028695836 @default.
• W57706274 cites W2033671250 @default.
• W57706274 cites W2034901905 @default.
• W57706274 cites W2054868397 @default.
• W57706274 cites W2063871813 @default.
• W57706274 cites W2080002617 @default.
• W57706274 cites W2094340308 @default.
• W57706274 cites W2105734704 @default.
• W57706274 cites W2118134037 @default.
• W57706274 cites W2125785272 @default.
• W57706274 cites W2127366531 @default.
• W57706274 cites W2150115013 @default.
• W57706274 cites W21608702 @default.
• W57706274 cites W2332976355 @default.
• W57706274 cites W2579656333 @default.
• W57706274 cites W573663564 @default.
• W57706274 hasPublicationYear "2012" @default.
• W57706274 type Work @default.
• W57706274 sameAs 57706274 @default.
• W57706274 citedByCount "0" @default.
• W57706274 crossrefType "dissertation" @default.
• W57706274 hasAuthorship W57706274A5084737250 @default.
• W57706274 hasConcept C114417882 @default.
• W57706274 hasConcept C134306372 @default.
• W57706274 hasConcept C136119220 @default.
• W57706274 hasConcept C137212723 @default.
• W57706274 hasConcept C155069649 @default.
• W57706274 hasConcept C202444582 @default.
• W57706274 hasConcept C33923547 @default.
• W57706274 hasConcept C42747912 @default.
• W57706274 hasConcept C5961521 @default.
• W57706274 hasConcept C78606066 @default.
• W57706274 hasConcept C79236096 @default.
• W57706274 hasConceptScore W57706274C114417882 @default.
• W57706274 hasConceptScore W57706274C134306372 @default.
• W57706274 hasConceptScore W57706274C136119220 @default.
• W57706274 hasConceptScore W57706274C137212723 @default.
• W57706274 hasConceptScore W57706274C155069649 @default.
• W57706274 hasConceptScore W57706274C202444582 @default.
• W57706274 hasConceptScore W57706274C33923547 @default.
• W57706274 hasConceptScore W57706274C42747912 @default.
• W57706274 hasConceptScore W57706274C5961521 @default.
• W57706274 hasConceptScore W57706274C78606066 @default.
• W57706274 hasConceptScore W57706274C79236096 @default.
• W57706274 hasLocation W577062741 @default.
• W57706274 hasOpenAccess W57706274 @default.
• W57706274 hasPrimaryLocation W577062741 @default.
• W57706274 hasRelatedWork W1970016609 @default.
• W57706274 hasRelatedWork W1994061581 @default.
• W57706274 hasRelatedWork W2053360298 @default.
• W57706274 hasRelatedWork W2611026033 @default.
• W57706274 hasRelatedWork W2737318976 @default.
• W57706274 hasRelatedWork W2746257945 @default.
• W57706274 hasRelatedWork W2785926876 @default.
• W57706274 hasRelatedWork W2815841711 @default.
• W57706274 hasRelatedWork W2881150100 @default.
• W57706274 hasRelatedWork W2952974507 @default.
• W57706274 hasRelatedWork W2963006598 @default.
• W57706274 hasRelatedWork W2963039459 @default.
• W57706274 hasRelatedWork W2963427800 @default.
• W57706274 hasRelatedWork W2995307386 @default.
• W57706274 hasRelatedWork W3014924691 @default.
• W57706274 hasRelatedWork W3041120743 @default.
• W57706274 hasRelatedWork W3103680687 @default.
• W57706274 hasRelatedWork W3104266525 @default.
• W57706274 hasRelatedWork W3105110639 @default.
• W57706274 hasRelatedWork W629609137 @default.
• W57706274 isParatext "false" @default.
• W57706274 isRetracted "false" @default.
• W57706274 magId "57706274" @default.
• W57706274 workType "dissertation" @default.