Sums of squares in hyperelliptic function fields
Dr. Marco Zaninelli, UPenn
Abstract: Building on work by Becher and Van Geel, we study sums of squares in function fields of hyperelliptic curves, mostly over hereditarily pythagorean fields. A refinement of their techniques allows us to obtain upper bound 2 for the Pythagoras number of certain such fields. As a consequence, we give a negative answer to Becher and Van Geel’s question whether Pythagoras number 2 for the function field of the elliptic curve X(X^2+1) implies that the base field K is infinity-hereditarily pythagorean or -1 belongs to K^2.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
