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On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups

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Buildings, Finite Geometries and Groups

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 10))

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Abstract

In this survey I sketch Behr–Harder reduction theory for reductive groups over global functions fields and briefly describe its applicability in the theory of S-arithmetic groups, notably homological and isoperimetric properties.

Subject Classifications: MSC 2010: Primary 20-02 Secondary 11F75, 14L15, 20G30, 20G35, 20J06, 51E24

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Authors and Affiliations

  1. Mathematisches Institut, Justus-Liebig-Universität Gießen, Arndtstraße 2, 35392, Gießen, Germany

    Köhl né Gramlich

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  1. Köhl né Gramlich
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Correspondence to Köhl né Gramlich .

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  1. Indian Statistical Institute, Mysore Road 8th Mile, Bangalore, 560 059, India

    N.S. Narasimha Sastry

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Gramlich, K.n. (2012). On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups. In: Sastry, N. (eds) Buildings, Finite Geometries and Groups. Springer Proceedings in Mathematics, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0709-6_4

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