Ginzburg, Kapranov and Vasserot conjectured the existence of equivariant elliptic cohomology theories. In this paper, to give a description of equivariant spectra of the theories, we study an intermediate theory, quasielliptic cohomology. We formulate a new category of orthogonal G−spectra and construct explicitly an orthogonal G−spectrum of quasi-elliptic cohomology in it. The idea of the construction can be applied to a family of equivariant cohomology theories, including Tate K-theory and generalized Morava E-theories. Moreover, this construction provides a functor from the category of global spectra to the category of orthogonal G−spectra. In addition, from it we obtain some new idea what global homotopy theory is right for constructing global elliptic cohomology theory.
Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions on it can be made in a neat way. This theory reflects the geometric nature of the Tate curve. In this paper we provide a systematic introduction of its construction and definition.
In this paper we define a family of theories, quasi-theories, motivated by quasi-elliptic cohomology. They can be defined from constant loop spaces. With them, the constructions on certain theories can be made in a neat way, such as those on generalized Tate K-theories. We set up quasi-theories and discuss their properties.
In this paper we construct orthogonal G−spectra up to a weak equivalence for the quasi-theory QE * n,G (−) corresponding to certain cohomology theories E. The construction of the orthogonal G−spectrum for quasielliptic cohomology can be applied to the constructions for quasi-theories.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.