Local diophantine properties of modular curves of D-elliptic sheaves

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Abstract

We study the existence of rational points on modular curves of D-elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some applications which include finding presentations for arithmetic groups arising from quaternion algebras, finding the equations of modular curves of D-elliptic sheaves, and constructing curves violating the Hasse principle.

Original languageEnglish (US)
Pages (from-to)115-140
Number of pages26
JournalJournal fur die Reine und Angewandte Mathematik
Volume2012
Issue number664
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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