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                <authority type="jury">Michel Brion [Rapporteur]</authority>
                <authority type="jury">Tyakal Nanjundiah Venkataramana [Rapporteur]</authority>
                <authority type="jury">Dan Segal</authority>
                <authority type="jury">Inna Capdeboscq</authority>
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                <term xml:lang="en">Profinite groups</term>
                <term xml:lang="en">Pseudo-Reductive groups</term>
                <term xml:lang="en">Bruhat-Tits theory</term>
                <term xml:lang="en">Affine buildings</term>
                <term xml:lang="en">Local fields</term>
                <term xml:lang="en">Linear algebraic groups</term>
                <term xml:lang="fr">Groupes pseudo-Réductifs</term>
                <term xml:lang="fr">Groupes profinis</term>
                <term xml:lang="fr">Théorie de Bruhat-Tits</term>
                <term xml:lang="fr">Immeubles affines</term>
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              <p>In this thesis, we are interested in the profinite and pro-p subgroups of a connected linear algebraic group defined over a local field. In the first chapter, we briefly summarize the Bruhat-Tits theory and introduce the notations necessary for this work. In the second chapter we find conditions equivalent to the existence of maximal compact subgroups of any connected linear algebraic group G defined over a local field K. In the third chapter, we obtain a conjugacy theorem of the maximal pro-p subgroups of G(K) when G is reductive. We describe these subgroups, more and more precisely, assuming successively that G is semi-simple, then simply connected, then quasi-split in addition. In the fourth chapter, we are interested in the pro-p presentations of a maximal pro-p subgroup of the group of rational points of a quasi-split semi-simple algebraic group G defined over a local field K. More specifically, we compute the minimum number of generators of a maximal pro-p subgroup. We obtain a formula which is linear in the rank of a certain root system, which depends on the ramification of the minimal extension L=K which splits G, thus making explicit the contributions of the Lie theory and of the arithmetic of the base field.</p>
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              <p>Dans cette thèse, nous nous intéressons aux sous-groupes profinis et pro-p d'un groupe algébrique linéaire connexe défini sur un corps local. Dans le premier chapitre, on résume brièvement la théorie de Bruhat-Tits et on introduit les notations nécessaires à ce travail. Dans le second chapitre, on trouve des conditions équivalentes à l'existence de sous-groupes compacts maximaux d'un groupe algébrique linéaire G connexe quelconque défini sur un corps local K. Dans le troisième chapitre, on obtient un théorème de conjugaison des sous-groupes pro-p maximaux de G(K) lorsque G est réductif. On décrit ces sous-groupes, de plus en plus précisément, en supposant successivement que G est semi-simple, puis simplement connexe, puis quasi-déployé. Dans le quatrième chapitre, on s'intéresse aux présentations d'un sous-groupe pro-p maximal du groupe des points rationnels d'un groupe algébrique G semi-simple simplement connexe quasi-déployé défini sur un corps local K. Plus spécifiquement, on calcule le nombre minimal de générateurs topologiques d'un sous-groupe pro-p maximal. On obtient une formule linéaire en le rang d'un certain système de racines, qui dépend de la ramification de l'extension minimale L=K déployant G, explicitant ainsi les contributions de la théorie de Lie et de l'arithmétique du corps de base.</p>
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