Silting modules

By Lidia Angeleri Hugel, F. Marks, Jorge Vit'oria. 2014

147 citations recorded by the source corpus.

We introduce the new concept of silting modules. These modu les generalise tilting modules over an arbitrary ring, as well as support τ-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten. We show that silting modules generate tors ion classes that provide left approximations, and that ever y partial silting module admits an analogue of the Bongartz co mplement. Furthermore, we prove that silting modules are in bijection with 2-term silting complexes and with certain tstructures and co-t-structures in the derived module categ ory. We also see how some of these bijections hold for silting comp lexes of arbitrary finite length.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/091d74bf260b070f361de8faa3ea3fd626351b25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Artificial Intelligence

J. Št’ovíček

In Geometry and Topology

Citations in the corpus

Torsion classes, wide subcategories and localisations (2015, result): “ctive}. We say that T is silting with respect to σif Dσ=gen(T). We say that T is silting if there exists a projective presentation σof T with respect to which T is silting. This concept was deﬁned in [AMV] in the category of all module s, but if T ∈ mod(A), our deﬁnition is easily seen to be equival”
Torsion pairs in silting theory (2016, unknown): “We refer to [Angeleri Hügel et al. 2016, Example 2.9 (2)] for details on the left adjacent co-t-structure.”
Realisation functors in tilting theory (2015, background): “2] that any silting complexM in D(A) following the definition in [8,78] is silting according to our definition.”