We investigate the category of K (h)-local spectra through the action of the Morava stabiliser
group. Using condensed mathematics, we give a model for the continuous action of this …

Using a form of Galois descent, we construct a family of spectral sequences computingthe
homotopy groups of the Picard space Picn whose 0th homotopy group is the Picard group of …

In this thesis, we study the homotopy theory of fixed points using methods from equivariant
homotopy theory. Given a compact topological space with the action of a p-group, the fixed …

We study the Picard group of Franke's category of quasi-periodic $ E_0E $-comodules for $
E $ a 2-periodic Landweber exact cohomology theory of height $ n $ such as Morava $ E …

We prove that the only separable commutative ring-objects in the stable module category of
a finite cyclic p-group G are the ones corresponding to subgroups of G. We also describe the …

We introduce the stable module∞-category for groups of type Φ as an enhancement of the
stable category defined by N. Mazza and P. Symonds. For groups of type Φ which act on a …

We recast many central results in chromatic homotopy theory as statements in spectral
algebraic geometry, as concerning certain spectral enhancements of the stack of formal …

One problem of interest in modular representation theory of finite groups is in computing the
group of endo-trivial modules. For p-groups, this group was originally computed by Carlson …

We prove $ p $-complete arc-descent results for finite projective modules and perfect
complexes over integral perfectoid rings. Using our results, we clarify a reduction argument …

We introduce notions of unramified and totally ramified maps in great generality-for
commutative rings, schemes, ring spectra, or derived schemes. We prove that the definition …