Mix-automatic sequences form a proper extension of the class of automatic sequences, and arise from a generalization of finite state automata where the input alphabet is state-dependent. In this paper we compare the class of mix-automatic sequences with the class of morphic sequences. For every polynomial φ we construct a mix-automatic sequence whose subword complexity exceeds φ. This stands in...

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the “Segre map”) of infinite loop spaces. Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced which establishe...

Let w be a morphic word over a finite alphabet Σ, and let ∆ be a nonempty subset of Σ. We study the behavior of maximal blocks consisting only of letters from ∆ in w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k’th maximal ∆-block in w. Then lim supk→∞(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a result, we s...

We construct three di erent spectra, and hence three generalized cohomology theories, associated to an algebraic variety X: the morphic spectrum ZX an E1-ring spectrum related to intersection theory when X is smooth; the multiplicative morphic spectrum MX and the holomorphic K-theory spectrum KX . The constructions use holomorphic maps from X into appropriate moduli spaces, and are functorial o...

The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over Q p form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of periodic points, and a morphic analogue of Jensen's formula.