manuel.ojanguren@epfl.ch, parimala@math.tifr.res.in

Submission: 2005, Jul 20, revised: 2005 Jul 25

Using geometric methods introduced by de Jong, we prove that if k is an algebraically closed field of characteristic zero and K an extension of k of transcendence degree two, then every central division algebra of prime degree over K is cyclic.

2000 Mathematics Subject Classification: 16K20, 14F22

Keywords and Phrases: cyclic division algebras, surfaces

Full text: dvi.gz 89 k, dvi 227 k, ps.gz 924 k, pdf.gz 361 k, pdf 397 k.