A geometric approach to absolute irreducibility of polynomials

Koyuncu, Fatih
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newton polytopes. For any field F; a polynomial f in F[x1, x2,..., xk] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F; i.e. irreducible over every algebraic extension of F. We present some new results giving integrally indecomposable classes of polytopes. Consequently, we have some new criteria giving infinitely many types of absolutely irreducible polynomials over arbitrary fields.


On the deformation chirality of real cubic fourfolds
Finashin, Sergey (Wiley, 2009-09-01)
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
A generic identification theorem for L*-groups of finite Morley rank
Berkman, Ayse; Borovik, Alexandre V.; Burdges, Jeffrey; Cherfin, Gregory (Elsevier BV, 2008-01-01)
This paper provides a method for identifying "sufficiently rich" simple groups of finite Morley rank with simple algebraic groups over algebraically closed fields. Special attention is given to the even type case, and the paper contains a number of structural results about simple groups of finite Morley rank and even type.
Kummer extensions of function fields with many rational places
Gülmez Temur, Burcu; Özbudak, Ferruh; Department of Mathematics (2005)
In this thesis, we give two simple and effective methods for constructing Kummer extensions of algebraic function fields over finite fields with many rational places. Some explicit examples are obtained after a practical search. We also study fibre products of Kummer extensions over a finite field and determine the exact number of rational places. We obtain explicit examples with many rational places by a practical search. We have a record (i.e the lower bound is improved) and a new entry for the table of v...
An identification theorem for groups of finite Morley rank and even type
Berkman, A; Borovik, AV (Elsevier BV, 2003-08-15)
The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Citation Formats
F. Koyuncu, “A geometric approach to absolute irreducibility of polynomials,” Ph.D. - Doctoral Program, Middle East Technical University, 2004.