id,collection,dc.contributor.author,dc.contributor.firstReferee,dc.contributor.furtherReferee,dc.contributor.gender,dc.date.accepted,dc.date.accessioned,dc.date.available,dc.date.issued,dc.description.abstract[en],dc.format.extent,dc.identifier.uri,dc.identifier.urn,dc.language,dc.rights.uri,dc.subject.ddc,dc.subject[en],dc.title,dc.type,dcterms.accessRights.dnb,dcterms.accessRights.openaire,dcterms.accessRights.proquest,dcterms.format,refubium.affiliation
"6ea004ab-6a67-48b9-af33-45e293b4423d","fub188/14","Hao, Yun","Esnault, Hélène","Groechenig, Michael","male","2019-05-20","2019-08-12T09:32:02Z","2019-08-12T09:32:02Z","2019","Let X/C be a smooth projective variety over the complex numbers. In the early 90's, Simpson established an equivalence between the category of local systems and that of the semi-stable Higgs bundles whose Chern class is zero. The correspondence between Higgs bundles and local systems can be viewed as a Hodge theorem for nonabelian cohomology. The theory is hence called the non-abelian Hodge theory, and sometimes is called the Simpson correspondence.
It has been a while to search for such a correspondence in positive characteristic. In this article, the following result is shown. Let X be an abelian variety over an algebraically closed field k of characteristic p > 0. Let X' be its Frobenius twist. Fix a natural number r, and consider the moduli stack (Higgs') of Higgs bundles on X' of rank r and the moduli stack (LocSys) of local systems on X of rank r. Then there are maps from (LocSys) and (Higgs') to a common base scheme B', which is an affine space over k. Moreover, there exists an étale surjective map U to B', such that after a base change to U, the two stacks (Higgs') and (LocSys) are isomorphic.
This result partially generalizes a previous result of Groechenig, where X is a curve, to higher dimensional varieties.","v, 45 Seiten","https://refubium.fu-berlin.de/handle/fub188/25261||http://dx.doi.org/10.17169/refubium-3966","urn:nbn:de:kobv:188-refubium-25261-7","eng","https://creativecommons.org/licenses/by/4.0/","500 Natural sciences and mathematics::510 Mathematics::513 Arithmetic||500 Natural sciences and mathematics::510 Mathematics::512 Algebra and number theory","Higgs Bundles||Local Systems||Hitchin Morphism||Positive Characteristic||Abelian Varieties","A Simpson Correspondence for Abelian Varieties in Positive Characteristic","Dissertation","free","open access","accept","Text","Mathematik und Informatik"