Frederik Marks
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View article: A functorial approach to rank functions on triangulated categories
A functorial approach to rank functions on triangulated categories Open
We study rank functions on a triangulated category 𝒞 via its abelianisation mod C \operatorname{mod}\mathcal{C} . We prove that every rank function on 𝒞 can be interpreted as an additive function on mod C \operatorname{mod}\mat…
View article: Lifting and restricting t‐structures
Lifting and restricting t‐structures Open
We explore the interplay between t‐structures in the bounded derived category of finitely presented modules and the unbounded derived category of all modules over a coherent ring using homotopy colimits. More precisely, we show that every …
View article: A functorial approach to rank functions on triangulated categories
A functorial approach to rank functions on triangulated categories Open
We study rank functions on a triangulated category $\mathcal{C}$ via its abelianisation $\operatorname{mod}\mathcal{C}$. We prove that every rank function on $\mathcal{C}$ can be interpreted as an additive function on $\operatorname{mod}\m…
View article: Lifting and restricting t-structures
Lifting and restricting t-structures Open
We explore the interplay between t-structures in the bounded derived category of finitely presented modules and the unbounded derived category of all modules over a coherent ring $A$ using homotopy colimits. More precisely, we show that ev…
View article: Flat ring epimorphisms and universal localizations of commutative rings
Flat ring epimorphisms and universal localizations of commutative rings Open
We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when su…
View article: Partial silting objects and smashing subcategories
Partial silting objects and smashing subcategories Open
We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated localis…
View article: A characterisation of 𝜏-tilting finite algebras
A characterisation of 𝜏-tilting finite algebras Open
We prove that a finite dimensional algebra is τ-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a τtilting finite algebra A there is a bijection between isomorphism classes of basic support…
View article: A characterisation of $τ$-tilting finite algebras
A characterisation of $τ$-tilting finite algebras Open
We prove that a finite dimensional algebra is $τ$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $τ$-tilting finite algebra $A$ there is a bijection between isomorphism classes of basic …
View article: A characterisation of $\tau$-tilting finite algebras
A characterisation of $\tau$-tilting finite algebras Open
We prove that a finite dimensional algebra is $\\tau$-tilting finite if and\nonly if it does not admit large silting modules. Moreover, we show that for a\n$\\tau$-tilting finite algebra $A$ there is a bijection between isomorphism\nclasse…
View article: Torsion pairs in silting theory
Torsion pairs in silting theory Open
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 a purity assumption. Moreover, in the cosilting c…
View article: Silting modules and ring epimorphisms
Silting modules and ring epimorphisms Open
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism whi…
View article: Silting modules and ring epimorphisms
Silting modules and ring epimorphisms Open
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism whi…
View article: Interactions between universal localisations, ring epimorphisms and tilting modules
Interactions between universal localisations, ring epimorphisms and tilting modules Open
The aim of this thesis is to study the interaction between universal localisations, ring epimorphisms and (generalised) tilting modules. We show that these concepts are intrinsically connected and that they provide various new applications…