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 …

Contraherent cosheaves are globalizations of cotorsion (or similar) modules over
commutative rings obtained by gluing together over a scheme. The category of contraherent …

We introduce new enhancements for the bounded derived category D b (Coh (X)) of
coherent sheaves on a suitable scheme X and for its subcategory P erf (X) of perfect …

This paper is a follow-up to arXiv: 2212.09639. We consider two algebraic settings of
comodules over a coring and contramodules over a topological ring with a countable base …

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 …

Homological mirror symmetry has its origins in theoretical physics but is now of great interest
in mathematics due to the deep connections it reveals between different areas of geometry …

We present a general construction of model category structures on the category C (Qco (X))
of unbounded chain complexes of quasi-coherent sheaves on a semi-separated scheme X …

Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …

Principal affine open subsets in affine schemes are an important tool in the foundations of
algebraic geometry. Given a commutative ring R, R-modules built from the rings of functions …

We define the notion of an infinitely generated tilting object of infinite homological dimension
in an abelian category. A one-to-one correspondence between∞-tilting objects in complete …