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On quadratic forms of height two and a theorem of Wadsworth |
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| Authors: | Detlev W. Hoffmann |
| Affiliation: | Aindorferstr. 84, D-80689 Munich, Germany |
| Abstract: | Let  and  be anisotropic quadratic forms over a field  of characteristic not  . Their function fields  and  are said to be equivalent (over  ) if  and  are isotropic. We consider the case where  and  is divisible by an  -fold Pfister form. We determine those forms  for which  becomes isotropic over  if  , and provide partial results for  . These results imply that if  and  are equivalent and  , then  is similar to  over  . This together with already known results yields that if  is of height  and degree  or  , and if  , then  and  are equivalent iff  and  are isomorphic over  . |
| Keywords: | Quadratic forms of height 2 function fields of quadratic forms equivalence of function fields isomorphism of function fields |
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