Elementary bounded generation for SLn${\rm SL}_n$ for global function fields and n⩾3$n\geqslant 3$

Abstract

AbstractThis paper shows that the group is boundedly elementary generated for and the ring of algebraic integers in a global function field. Contrary to previous statements for number fields and earlier statements for global function fields, the bounds proven in this paper for elementary bounded generation are independent of the underlying global function field and only depend on the integer . Combining our main result with earlier results, we further establish that elementary bounded generation always has bounds independent from the global field in question, only depending on .