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Title:  Algebraic Curves Over Supersimple Fields 
Author(s):  MartinPizarro, Amador 
Doctoral Committee Chair(s):  Pillay, Anand 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  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 jinvariant is sgeneric over empty has a rational point over K which is sgeneric over the set of parameters used to define the curve. Note that a point in a variety over K is sgeneric over a given set of parameters A if the SUrank 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 sgeneric 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, C1fields) are studied. Moreover, a description of quadratic forms over supersimple fields is given. 
Issue Date:  2003 
Type:  Text 
Language:  English 
Description:  76 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2003. 
URI:  http://hdl.handle.net/2142/86828 
Other Identifier(s):  (MiAaPQ)AAI3111578 
Date Available in IDEALS:  20150928 
Date Deposited:  2003 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois