612 research outputs found

    The twisted forms of a semisimple group over an fq-curve

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    Let C be a smooth, projective and geometrically connected curve defined over a finite field Fq . Given a semisimple C −S-group scheme G where S is a finite set of closed points of C, we describe the set of (OS-classes of) twisted forms of G in terms of geometric invariants of its fundamental group F (G)

    On the genera of semisimple groups defined over an integral domain of a global function field

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    Let K=Fq(C)K=\mathbb{F}_q(C) be the global function field of rational functions over a smooth and projective curve CC defined over a finite field Fq\mathbb{F}_q. The ring of regular functions on CSC-S where SS \neq \emptyset is any finite set of closed points on CC is a Dedekind domain OS\mathcal{O}_S of KK. For a semisimple OS\mathcal{O}_S-group G\underline{G} with a smooth fundamental group F\underline{F}, we aim to describe both the set of genera of G\underline{G} and its principal genus (the latter if GOSK\underline{G} \otimes_{\mathcal{O}_S} K is isotropic at SS) in terms of abelian groups depending on OS\mathcal{O}_S and F\underline{F} only. This leads to a necessary and sufficient condition for the Hasse local-global principle to hold for certain G\underline{G}. We also use it to express the Tamagawa number τ(G)\tau(G) of a semisimple KK-group GG by the Euler Poincar\'e invariant. This facilitates the computation of τ(G)\tau(G) for twisted KK-groups.Comment: 18 page

    The Geometric Gauss–Dedekind

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    Human leukocyte antigen supertype matching after myeloablative hematopoietic cell transplantation with 7/8 matched unrelated donor allografts: a report from the Center for International Blood and Marrow Transplant Research

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    The diversity of the human leukocyte antigen (HLA) class I and II alleles can be simplified by consolidating them into fewer supertypes based on functional or predicted structural similarities in epitope-binding grooves of HLA molecules. We studied the impact of matched and mismatched HLA-A (265 versus 429), -B (230 versus 92), -C (365 versus 349), and -DRB1 (153 versus 51) supertypes on clinical outcomes of 1934 patients with acute leukemias or myelodysplasia/myeloproliferative disorders. All patients were reported to the Center for International Blood and Marrow Transplant Research following single-allele mismatched unrelated donor myeloablative conditioning hematopoietic cell transplantation. Single mismatched alleles were categorized into six HLA-A (A01, A01A03, A01A24, A02, A03, A24), six HLA-B (B07, B08, B27, B44, B58, B62), two HLA-C (C1, C2), and five HLA-DRB1 (DR1, DR3, DR4, DR5, DR9) supertypes. Supertype B mismatch was associated with increased risk of grade II-IV acute graft-versus-host disease (hazard ratio =1.78, P=0.0025) compared to supertype B match. Supertype B07-B44 mismatch was associated with a higher incidence of both grade II-IV (hazard ratio=3.11, P=0.002) and III-IV (hazard ratio=3.15, P=0.01) acute graft-versus-host disease. No significant associations were detected between supertype-matched versus -mismatched groups at other HLA loci. These data suggest that avoiding HLA-B supertype mismatches can mitigate the risk of grade II-IV acute graft-versus-host disease in 7/8-mismatched unrelated donor hematopoietic cell transplantation when multiple HLA-B supertype-matched donors are available. Future studies are needed to define the mechanisms by which supertype mismatching affects outcomes after alternative donor hematopoietic cell transplantation
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