Real Algebraic Number Theory I: Diophantine Approximation Groups

Details Real Algebraic Number Theory I: Diophantine Approximation Groups Real Algebraic Number Theory I: Diophantine Approximation Groups

2012-01-12

arxiv.org/abs/1201.2708v1

Mathematics

Number Theory

Scientific paper

The is the first of three papers introducing a paradigm within which global algebraic number theory for the reals may be formulated so as to make possible the synthesis of algebraic and transcendental number theory into a coherent whole. We introduce diophantine approximation groups and their associated Kronecker foliations, using them to provide new algebraic and geometric characterizations of K-linear and algebraic dependence. As a consequence we find reformulations -- as algebraic and geometric (graph) rigidities -- of the Theorems of Baker and Lindemann-Weierstrass, the Logarithm Conjecture and the Schanuel Conjecture. There is an Appendix describing diophantine approximation groups as model theoretic types.

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