Approximation theory is a fundamental tool in order to study the representation theory of a
ring R. Roughly speaking, it consists in determining suitable additive or abelian …

Any Thomason filtration of a commutative ring yields (at least) two t-structures in the derived
category of the ring, one of which is compactly generated [19],[20]. We study the hearts of …

We classify all compactly generated t-structures in the unbounded derived category of an
arbitrary commutative ring, generalizing the result of Alonso Tarrío et al.(J Algebra 324 (3) …

This thesis deals with the general problem of determining when the heart $\mathcal {H} $ of
a t-structure in a triangulated category $\mathcal {D} $ is a Grothendieck or a module …

T-structures on triangulated categories were introduced in the early eighties by Beillison,
Berstein and Deligne in their study of the perverse sheaves on an algebraic or an analytic …

Let $ R $ be a commutative Noetherian ring and let $\mathcal D (R) $ be its (unbounded)
derived category. We show that all compactly generated t-structures in $\mathcal D (R) …

We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

In this work, we shall study in a purely model-independent fashion the∞-category of mixed
graded modules over a ring of characteristic 0, as defined by D. Calaque, T. Pantev, M …

Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of
support, the structure of both Mod (R) and D (R). We show that, just like in Mod (R), the …

Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …