We introduce the notion of a prism, which may be regarded as a" deperfection" of the notion
of a perfectoid ring. Using prisms, we attach a ringed site---the prismatic site---to a p-adic …

Let G be a finite group and let F be a family of subgroups of G. We introduce a class of G-
equivariant spectra that we call F-nilpotent. This definition fits into the general theory of …

One fundamental consequence of a scheme-descent results which hold in the setting of
derived algebraic geometry but not in classical algebraic geometry. Our main applications …

We develop a full 6-functor formalism for $ p $-torsion\'etale sheaves in rigid-analytic
geometry. More concretely, we use the recently developed condensed mathematics by …

We study a Grothendieck topology on schemes which we call the arc-topology. This
topology is a refinement of the v-topology (the pro-version of Voevodsky'sh-topology), where …

This paper starts with an exposition of descent-theoretic techniques in the study of Picard
groups of E∞–ring spectra, which naturally lead to the study of Picard spectra. We then …

Schlichting conjectured that the negative K-groups of small abelian categories vanish and
proved this for noetherian abelian categories and for all abelian categories in degree-1-1 …

We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …

Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

We develop a general theory of higher semiadditive Fourier transforms that includes both
the classical discrete Fourier transform for finite abelian groups at height-modules [-12pc] …