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Pillay, Anand Martin-Pizarro, Amador 2015-09-28T15:19:44Z 2015-09-28T15:19:44Z 10000-01-01 2003 2003 In this work we are concerned with algebraic curves over supersimple fields. First it is proved that an elliptic curve defined over a supersimple field K whose j-invariant is s-generic over empty has a rational point over K which is s-generic over the set of parameters used to define the curve. Note that a point in a variety over K is s-generic over a given set of parameters A if the SU-rank of the point over A is equal to SU(K) times the dimension of the variety. The same statement as above holds for hyperelliptic curves defined over a supersimple field whose modulus is s-generic over empty . The proof requires a complete description of the smooth models of these curves in all characteristics as well as of the transformations between these curves. Finally, it is shown that for finite Galois extensions of K, the first cohomology group of the Galois group with coefficients in an elliptic curve defined over K is finite. Some similarities and division lines between supersimple fields and other fields with similar cohomological behaviour (for example, C1-fields) are studied. Moreover, a description of quadratic forms over supersimple fields is given. Made available in DSpace on 2015-09-28T15:19:44Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3111578.pdf: 4064838 bytes, checksum: db706bbbeac94a73f1d690f6200c4841 (MD5) Previous issue date: 2003 Embargo set by: Seth Robbins for item 88109 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 76 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003. http://hdl.handle.net/2142/86828 (MiAaPQ)AAI3111578 eng Mathematics Algebraic Curves Over Supersimple Fields text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.