Affine Deligne-Lusztig varieties in affine flag varieties

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.Comment: 44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of

Dimensions of some affine Deligne-Lusztig varieties

This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties X_mu(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of superbasic b. In the affine flag manifold, we prove a formula that reduces the dimension question for X_x(b) with b in the split torus to computations of dimensions of intersections of Iwahori orbits with orbits of the unipotent radical. Calculations using this formula allow us to verify a conjecture of Reuman in many new cases, and to make progress toward a generalization of his conjecture.Comment: 51 pages, 12 figure

A Prospective Pilot Study to Identify a Myocarditis Cohort who may Safely Resume Sports Activities 3 Months after Diagnosis

International cardiovascular society recommendations to return to sports activities following acute myocarditis are based on expert consensus in the absence of prospective studies. We prospectively enrolled 30 patients with newly diagnosed myocarditis based on clinical parameters, laboratory measurements and cardiac magnetic resonance imaging with mildly reduced or pre served left ventricular ejection fraction (LVEF) with a follow-up of 12 months. Cessation of physical activity was recommended for 3 months. The average age was 35 (19–80) years with 73% male patients. One case of non-sustained ventricular tachycardia was recorded during 48-h-Holter electrocardiogram. Except for this case, all patients were allowed to resume physical exercise after 3 months. At 6- (n = 26) and 12-month (n = 19) follow-up neither cardiac events nor worsening LVEF were recorded. The risk of cardiac events at 1 year after diagnosis of myocarditis appears to be low after resumption of exercise after 3 months among patients who recover from acute myocarditis

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Mutations in PINK1 and Parkin Impair Ubiquitination of Mitofusins in Human Fibroblasts

PINK1 and Parkin mutations cause recessive Parkinson's disease (PD). In Drosophila and SH-SY5Y cells, Parkin is recruited by PINK1 to damaged mitochondria, where it ubiquitinates Mitofusins and consequently promotes mitochondrial fission and mitophagy