We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme
is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More …

We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-
coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent …

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the
pullback construction f↦ f⁎ implements an equivalence between the discrete category of …

Let $ X $ be a Noetherian scheme, $\mathbf {K}(\operatorname {Flat} X) $ be the homotopy
category of flat quasi-coherent $\mathcal {O} _X $-modules and $\mathbf {K} …

We show how derived categories build bridges across the current mathematical mainstream,
linking geometric and algebraic, commutative and noncommutative, local and global banks …

Semi-Infinite Geometry is a theory of" doubly infinite-dimensional" geometric or topological
objects. In this book the author explains what should be meant by an algebraic variety of …

If X is a quasi-compact and quasi-separated scheme, the category Qcoh (X) of quasi-
coherent sheaves on X is locally finitely presented. Therefore categorical flat quasi-coherent …

Many homotopy-coherent algebraic structures can be described by Segal-type limit
conditions determined by an “algebraic pattern”, by which we mean an∞-category equipped …

The aim of this work is to give a generalization of Gabriel's Theorem on coherent sheaves to
coherent twisted sheaves on noetherian schemes. We start by showing that we can recover …

In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-
coherent sheaf over a scheme (X, OX). Indeed we prove something more general. We define …