Scientific Work

1.

Semistable Elliptic Curves and Fermat Last Theorem (master Thesis in Greek)

2.

The group of Automorphisms of the Function Fields of the Curves xⁿ+y^m+1=0 J. of Number Theory 72, p.110-136 (1998)

3.

The group of automorphisms of function fields of the curves yⁿ=f(x). To appear in J. of Algebra June or July 1999

4.

Automorphisms of Mumford Curves in posititve characteristic (together with G. Cornelissen)

My master thesis (1) was about the Frey construction of a counterexample to Taniyama-Shimura conjecture using the negation of Fermat Last Theorem.

In (2), we have studied the group of automorphisms G_n,m of function fields of the curves $% x^n+y^m+1=0,\,$over an algebraically closed field k of characteristic $% p\geq 0\,$for n>m, and $p\nmid n,m.\,$The case n=m was studied by Leopoldt.

In (3) we use the ideas of Accola on strongly branched covers in order to give sufficient conditions for C_n=Gal(F/k(x)) to be a normal subgroup of G where $F\,$is the function field of the curve yⁿ=f(x) and $G\,$the group of automorphisms of F. Then the group $G\,$is studied as a group extension of a finite known subgroup of PGL(2,k) by abelian kernel $% C_n.\,$The corresponding 2-cohomology class of this extension was determined in means of the polynomial $f(x).\,$This work generalizes the paper of R. Brandt and H. Stichtenoth on the group of automorphisms of hyperelliptic curves and the latter work of R. Brand.

In (4) we prove that the number of automorphisms of a Mumford curve of genus $g\geq 2$ over a field of characteristic p>0 is bounded by $2\sqrt{g}(\sqrt{g}+1)^2$, i.e., by a polynomial in $\sqrt{g}$ of degree 3, and this bound is attained for all fixed p for infinitely many curves. The proof involves a detailed study of the structure of the automorphism group as an HHN-extension of a tree of finite subgroups of PGL(2,k). As an application, we show that automorphisms of certain Drinfeld modular curves preserve the cusps.