@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ Let p be a prime. The subject of this thesis is the p-adic Langlands correspondence. If V is a p-adic representation of dimension 2 of the group Gal(\\bar{Qp}/Qp), it is known how to associate to it a continuous p-adic representation B(V) of GL₂(Qp). If F is a non-trivial finite extension of Qp, the issue of associating p-adic representations of GL₂(F) to p-adic representations of dimension 2 of Gal(\\bar{Qp}/F) in the spirit of a local Langlands correspondence appears much more delicate. In this text we consider a class of p-adic Banach spaces, endowed with a continuous linear action of GL₂(F), which are obtained as universal unitary completions of certain locally Qp-analytic representations of GL₂(F). Such representations are likely to play an important role in a future local p-adic Langlands correspondence for GL₂(F). The main result of this thesis is proved in Chapter 3 and generalizes some previous results of Berger and Breuil. It consists in an explicit description of these universal unitary completions by means of a certain class of continuous functions on F. In order to do this, we introduce in Chapter 2 a class of Banach spaces of functions of class C^r, where r is a positive rational number, as well as their dual spaces of distributions of order r. We build a Banach base and we give a criterion for telling when a linear form defined on a space of locally Qp-polynomial functions extends to a distribution of order r. As a consequence, we generalize some classical results due to Amice-Vélu and Vishik. In Chapter 4 we exhibit cases of non-nullity for these universal unitary completions, by an explicit construction of invariant lattices. This also provides new instances of the Breuil-Schneider conjecture about the equivalence between the existence of invariant norms on certain locally algebraic representations of GL_d(F) and the existence of certain De Rham representations of Gal(\\bar{Qp}/F). """ ; dct:identifier "NNT: 2012PA112360" ; dct:issued "2026-05-12T06:21:34.432184"^^xsd:dateTime ; dct:language "fr" ; dct:modified "2026-05-12T06:21:34.432189"^^xsd:dateTime ; dct:publisher ; dct:title "p-adic analysis and universal unitary completion for GL₂(F)" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "analyse-p-adique", "breuil-schneider-conjecture", "complete-unitaire-universel", "conjecture-de-breuil-schneider", "distribution-of-order-r", "distributions-dordre-r", "fonctions-de-classe-cr", "function-of-class-cr", "infoeu-reposemanticsdoctoralthesis", "langlands-p-adique", "locally-analytic-representation", "mathmath-gmmathematics-mathgeneral-mathematics-mathgm", "p-adic-analysis", "p-adic-langlands-correspondence", "representation-localement-analytique", "theses", "unitary-universal-completion" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-12T06:21:34.435938"^^xsd:dateTime ; dct:modified "2026-05-12T06:21:34.378610"^^xsd:dateTime ; dct:title "p-adic analysis and universal unitary completion for GL₂(F)" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .