Frederik Marks

Torsion classes, wide subcategories and localisations

For a finite-dimensional algebra A, we establish correspondences between torsion classes and wide subcategories in mod(A). In case A is representation finite, we obtain an explicit bijection between these two classes of subcategories. Moreover, we translate our results to the language of ring epimorphisms and universal localisations. It turns out that universal localisations over representation finite algebras are classified by torsion classes and support τ-tilting modules.

Torsion pairs in silting theory

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 case the previous conditions are related to the coaisle of the t-structure being a definable subcategory. If we further assume our triangulated category to be algebraic, it follows that the heart of any nondegenerate compactly generated t-structure is a Grothendieck category.

Homological embeddings for preprojective algebras

For a fixed finite dimensional algebra A, we study representation embeddings of the form

Universal localisations via silting

mod(B)\rightarrow mod(A)

From ring epimorphisms to universal localisations

mod(B)→mod(A). Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only Ext

Flat ring epimorphisms and universal localisations of commutative rings

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