References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

In the setting of compactly generated triangulated categories, we show that the heart of a
(co) silting t-structure is a Grothendieck category if and only if the (co) silting object satisfies …

We classify all tilting and cotilting classes over commutative noetherian rings in terms of
descending sequences of specialization closed subsets of the Zariski spectrum …

Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …

We study the class of modules, called cosilting modules, which are defined as the
categorical duals of silting modules. Several characterizations of these modules and …

We introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-
cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules …

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …