Search

Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the integrality of generic irreducible locally algebraic representations. In this article, we prove the sufficiency of Emerton's conditions for some tamely ramified locally algebraic representations of $\mathrm{GL}_{2}(D)$ where $D$ is a $p$-adic division algebra., Comments are welcome

BACKGROUND: A paucity of data regarding the implications of postoperative hematoma formation on outcomes after shoulder arthroplasty exists. Previous studies on major joint arthroplasty have associated postoperative hematoma formation with high rates of prosthetic joint infection (PJI) and reoperation. METHODS: A total of 6,421 shoulder arthroplasty cases were retrospectively reviewed from an institutional database (5,941 primary cases, 480 revision) between December 2008 and July 2017. Patients who developed a postoperative hematoma were identified through direct chart review. Cases with a history of shoulder infection treated with explant and antibiotic spacer placement were excluded. Demographics, surgical characteristics, treatment course, and outcomes were collected. RESULTS: Hematoma occurred in 105 (1.6%; 105/6421) cases within the first three postoperative weeks and was more common following revision (3.3%; 16/480) compared to primary cases (1.5 %; 89/5941; P=0.002). Overall, postoperative shoulder hematoma was successfully managed with nonoperative treatment in 87% of cases via observation (62%, 62/105) and aspiration (25%, 26/105). A total of 14 patients (0.22%, 14/6421) underwent reoperation for hematoma. Eight patients (7.6%, 8/105) that required reoperation for hematoma were diagnosed with PJI. CONCLUSION: Postoperative hematoma is a complication of shoulder arthroplasty. While many postoperative hematomas can be managed without operative intervention, this analysis reiterates the association between hematoma formation and the development of PJI.

The 6-minute walk test (6MWT) is a test that is frequently used in the assessment of patients with a wide range of cardiorespiratory conditions. It consists of measuring the maximal distance that the assessed individual is able to walk in 6 minutes. This is used as a surrogate indicator of disease presence and progression, as well as to assess the outcome of an intervention. Clear advantages of this exercise test include the fact that it is sub-maximal, which by being below the patient’s maximal threshold is more reflective of a patient’s everyday experience (especially as compared to its more extensive counterpart, the cardiopulmonary exercise test) and the ease with which it is carried out – all it requires is a hallway ideally 30m in length. However, in many ways these advantages also constitute the test’s main drawbacks: it lacks consistency and standardisation between studies, and whilst a useful surrogate indicator in many diseases it reveals little about a disease’s underlying pathophysiology. Pulmonary fibrosis (PF) is a progressive, irreversible interstitial lung disease characterised by extensive scarring and fibrous tissue in the lungs progressively leading to mortality. Whilst identifiable causes include environmental pollution, connective tissue diseases and infections, the most common cause is idiopathic (idiopathic pulmonary fibrosis, IPF). PF patients present in the clinic with breathlessness, chronic dry cough, fatigue, and weight loss. These symptoms severely compromise their quality of everyday life. Currently, a therapeutic cure for PF is not available and treatment options remain limited and are mainly focused on symptom relief and slow down of disease progression. Whilst the change in 6-minute walk distance (6MWD) is frequently used as a primary or secondary outcome in clinical trials, there has not been a recent systematic review to date assessing the test’s association with mortality in patients with PF, despite established associations between 6MWT parameters and prognosis in many diseases – a decline in 6MWD is a strong predictor of disease progression, and baseline 6MWD correlates well with a variety of lung function tests. A systematic approach will be helpful in outlining not only the test’s utility, but also its main weaknesses, in the hope of informing how these may be addressed.

Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue field of $F$ extending the earlier results of authors for $F$ unramified over $\mathbb{Q}_{p}$. The construction is uniform and uses the theory of diagrams of Breuil and Pa\v{s}k$\mathrm{\bar{u}}$nas., Comment: 8 pages

Let $F$ be a non-archimedean local field of residual characteristic $p>3$ and residue degree $f>1$. We study a certain type of diagram, called \emph{cyclic diagrams}, and use them to show that the universal supersingular modules of $\mathrm{GL}_{2}(F)$ admit infinitely many non-isomorphic irreducible admissible quotients., 11 pages

We use a Diamond diagram attached to a $2$-dimensional reducible split mod $p$ Galois representation of $\mathrm{Gal}(\overline{\mathbb{Q}_{p}}/\mathbb{Q}_{p^{2}})$ to construct a non-admissible smooth irreducible mod $p$ representation of $GL_{2}(\mathbb{Q}_{p^{2}})$ following the approach of Daniel Le., Comment: 6 pages

Sei K eine endliche Erweiterung von Q_p mit dem Ring der ganzen Zahlen o, und sei H_0 ein formaler o-Modul von endlicher Höhe über einem separablen Abschluß des Restklassenkörpers von K. Der Lubin-Tate-Modulraum X_m klassifiziert die Deformationen von H_0 zusammen mit Level-m-Struktur. In dieser Doktorarbeit studieren wir einen besonderen Typ p-adischer Darstellungen, die sich aus der Aktion von Aut(H_0) auf bestimmten äquivarianten Vektorbündeln auf der generischen Faser von X_m ergeben. F ür alle Level m zeigen wir, daß der Fréchet-Raum der globalen Schnitte dieser Vektorbündel dual zu einer lokal K-analytischen Darstellung von Aut(H_0) ist und die vorherigen Ergebnisse von J. Kohlhaase im den Fall K = Q_p und m = 0 verallgemeinern. Als ein erster Schritt, um diese Darstellungen besser zu verstehen, berechnen wir ihre lokal endlichen Vektoren. Im Wesentlichen entstehen alle lokal endlichen Vektoren durch Zurückziehen von globalen Schnitten des projektiven Raums über den Gross-Hopkins-Periodenmorphismus. Let K be a finite extension of Q_p with ring of integers o, and let H_0 be a formal o-module of finite height over a separable closure of the residue class field of K. The Lubin-Tate moduli space X_m classifies deformations of H_0 equipped with level-m-structure. In this thesis, we study a particular type of p-adic representations originating from the action of Aut(H_0) on certain equivariant vector bundles on the generic fibre of X_m . We show that, for arbitrary level m, the Fréchet space of the global sections of these vector bundles is dual to a locally K-analytic representation of Aut(H_0) generalizing previous results of J. Kohlhaase in the case K = Q_p and m = 0. To get a better understanding of these representations, we compute their locally finite vectors. Essentially, all locally finite vectors arise from the global sections over the projective space via pullback along the Gross-Hopkins period map. Dissertation, Universität Duisburg-Essen, 2018

The Lubin-Tate moduli space $X_{0}^{\text{rig}}$ is a $p$-adic analytic open unit polydisc which parametrizes deformations of a formal group $H_{0}$ of finite height defined over an algebraically closed field of characteristic $p$. It is known that the natural action of the automorphism group $\text{Aut}(H_{0})$ on $X^{\text{rig}}_{0}$ gives rise to locally analytic representations on the topological duals of the spaces $H^{0}(X^{\text{rig}}_{0},(\mathcal{M}^{s}_{0})^{\mathrm{rig}})$ of global sections of certain equivariant vector bundles $(\mathcal{M}^{s}_{0})^{\mathrm{rig}}$ over $X^{\mathrm{rig}}_{0}$. In this article, we show that this result holds in greater generality. On the one hand, we work in the setting of deformations of formal modules over the valuation ring of a finite extension of $\mathbb{Q}_{p}$. On the other hand, we also treat the case of representations arising from the vector bundles $(\mathcal{M}^{s}_{m})^{\mathrm{rig}}$ over the deformation spaces $X^{\mathrm{rig}}_{m}$ with Drinfeld level-$m$-structures. Finally, we determine the space of locally finite vectors in $H^{0}(X^{\text{rig}}_{m},(\mathcal{M}^{s}_{m})^{\mathrm{rig}})$. Essentially, all locally finite vectors arise from the global sections of invertible sheaves over the projective space via pullback along the Gross-Hopkins period map., Comment: 40 pages. Introduction has been rewritten. Remark 3.4.7 has been added. To be published in Israel Journal of Mathematics

The Lubin-Tate moduli space $X_{0}^{\text{rig}}$ is a $p$-adic analytic open unit polydisc which parametrizes deformations of a formal group $H_{0}$ of finite height defined over an algebraically closed field of characteristic $p$. It is known that the natural action of the automorphism group $\text{Aut}(H_{0})$ on $X^{\text{rig}}_{0}$ gives rise to locally analytic representations on the topological duals of the spaces $H^{0}(X^{\text{rig}}_{0},(\mathcal{M}^{s}_{0})^{\mathrm{rig}})$ of global sections of certain equivariant vector bundles $(\mathcal{M}^{s}_{0})^{\mathrm{rig}}$ over $X^{\mathrm{rig}}_{0}$. In this article, we show that this result holds in greater generality. On the one hand, we work in the setting of deformations of formal modules over the valuation ring of a finite extension of $\mathbb{Q}_{p}$. On the other hand, we also treat the case of representations arising from the vector bundles $(\mathcal{M}^{s}_{m})^{\mathrm{rig}}$ over the deformation spaces $X^{\mathrm{rig}}_{m}$ with Drinfeld level-$m$-structures. Finally, we determine the space of locally finite vectors in $H^{0}(X^{\text{rig}}_{m},(\mathcal{M}^{s}_{m})^{\mathrm{rig}})$. Essentially, all locally finite vectors arise from the global sections of invertible sheaves over the projective space via pullback along the Gross-Hopkins period map., 40 pages. Introduction has been rewritten. Remark 3.4.7 has been added. To be published in Israel Journal of Mathematics