Introducing Global Groups
When studying cohomology theories, certain algebro-geometric groups appear naturally: formal groups (Quillen), elliptic curves (TMF), and algebraic tori. We present a uniform framework in globally equivariant homotopy theory in which these connections arise from a single adjunction. The framework generalizes algebraic groups and applies at arbitrary chromatic height. For example, it induces an equivalence between complex-oriented global $E_\infty$-ring spectra and spectral global group laws. As a proof of concept, we compute the space of $E_\infty$-endomorphisms of global complex K-theory by reducing to automorphisms of the multiplicative group.