Jens Hornbostel

In recent years, several people studied real topological Hochschild homology THR as a C_2-equivariant refinement of THH. This is in analogy with real or hermitian K-theory refining usual complex or algebraic K-theory. We recall the definitions of THH and THR, as well as some basic facts and
computations. Then we discuss more recent results like base change and descent for the Z/2-isovariant étale topology. We also provide computations of THR for the projective line (with and without
involution) and higher dimensional projective spaces. This is joint work with Doosung Park.