11d4111g0511f1111f8011g18 algebraicnumbertheory arithmeticalgebraicgeometry(diophantinegeometry) arithmeticaspectsofmodularandshimuravarieties diophantineequations discontinuousgroupsandautomorphicforms ellipticcurvesoverglobalfields fermat'slasttheorem galoisrepresentations higherdegreeequations;fermat'sequation numbertheory