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

Linsitinib, an IGF-1R inhibitor, attenuates disease development and progression in a model of thyroid eye disease

IntroductionGraves’ disease (GD) is an autoimmune disorder caused by autoantibodies against the thyroid stimulating hormone receptor (TSHR) leading to overstimulation of the thyroid gland. Thyroid eye disease (TED) is the most common extra thyroidal manifestation of GD. Therapeutic options to treat TED are very limited and novel treatments need to be developed. In the present study we investigated the effect of linsitinib, a dual small-molecule kinase inhibitor of the insulin-like growth factor 1 receptor (IGF-1R) and the Insulin receptor (IR) on the disease outcome of GD and TED.MethodsLinsitinib was administered orally for four weeks with therapy initiating in either the early (“active”) or the late (“chronic”) phases of the disease. In the thyroid and the orbit, autoimmune hyperthyroidism and orbitopathy were analyzed serologically (total anti-TSHR binding antibodies, stimulating anti TSHR antibodies, total T4 levels), immunohistochemically (H&E-, CD3-, TNFa- and Sirius red staining) and with immunofluorescence (F4/80 staining). An MRI was performed to quantify in vivo tissue remodeling inside the orbit.ResultsLinsitinib prevented autoimmune hyperthyroidism in the early state of the disease, by reducing morphological changes indicative for hyperthyroidism and blocking T-cell infiltration, visualized by CD3 staining. In the late state of the disease linsitinib had its main effect in the orbit. Linsitinib reduced immune infiltration of T-cells (CD3 staining) and macrophages (F4/80 and TNFa staining) in the orbita in experimental GD suggesting an additional, direct effect of linsitinib on the autoimmune response. In addition, treatment with linsitinib normalized the amount of brown adipose tissue in both the early and late group. An in vivo MRI of the late group was performed and revealed a marked decrease of inflammation, visualized by 19F MR imaging, significant reduction of existing muscle edema and formation of brown adipose tissue.ConclusionHere, we demonstrate that linsitinib effectively prevents development and progression of thyroid eye disease in an experimental murine model for Graves’ disease. Linsitinib improved the total disease outcome, indicating the clinical significance of the findings and providing a path to therapeutic intervention of Graves’ Disease. Our data support the use of linsitinib as a novel treatment for thyroid eye disease

Algebraic geometry I: schemes : with examples and exercises

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get started, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. For the second edition, several mistakes and many smaller errors and misprints have been corrected. Contents Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples About the Authors Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt