46 citations · 95 across the 26 of their papers we have counts for
30 papers
Semi-Bousfield classes and nonmonotone perversities
Dolors Herbera, Michal Hrbek, Giovanna Le Gros
In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive deg…
Proxy smallness meets -structures
Michal Hrbek, Pat Lank, Giovanna Le Gros +1
We introduce a notion of proxy smallness for -structures on triangulated categories associated to a Noetherian scheme. Specifically, the theory is developed in the presence of t…
On silting complexes associated to n-silting modules
Michal Hrbek, Jiangsheng Hu, Rongmin Zhu
We show that any (n+1)-term silting complex whose intermediate cohomology vanishes gives rise to an n-silting module, as recently introduced by Mao. Specializing to commutative noe…
Nonexistence of singly compactly generated -structures for schemes
Anirban Bhaduri, Timothy De Deyn, Michal Hrbek +2
We show the first instances of schemes whose standard aisles on their derived category of quasi-coherent sheaves are not singly compactly generated.
Telescope conjecture for quiver representations over artinian rings
Michal Hrbek, Enrico Sabatini
Let be the derived category of representations of a small category over a commutative noetherian ring . We study the homotopically smashing t-structures on…
Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions
Souvik Dey, Michal Hrbek, Giovanna Le Gros
Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstru…
Perfectly generated -structures for algebraic spaces
Michal Hrbek, Pat Lank, Simone Pizzirani
This work studies -structures for the derived category of complexes with quasi-coherent cohomology on algebraic spaces. The main result shows that the relative standard -stru…
Mutation and the Gabriel spectrum
Michal Hrbek, Sergio Pavon, Jorge Vitória
Mutations occur in multiple algebraic contexts, often enjoying good combinatorial properties. In this paper we study mutations of pure-injective cosilting objects in compactly gene…
Cotorsion pairs and Tor-pairs over commutative noetherian rings
Dolors Herbera, Michal Hrbek, Giovanna Le Gros
For a commutative noetherian ring , we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is don…
The finite type of modules of bounded projective dimension and Serre's conditions
Michal Hrbek, Giovanna Le Gros
Let be a commutative noetherian ring. We prove that the class of modules of projective dimension bounded by is of finite type if and only if satisfies Serre's condition…
Telescope conjecture via homological residue fields with applications to schemes
Michal Hrbek
For a big tt-category, we give a characterization of the Telescope Conjecture (TC) in terms of definable tensor-ideals generated by homological residue fields. We formulate a stalk…
Product-complete tilting complexes and Cohen-Macaulay hearts
Michal Hrbek, Lorenzo Martini
We show that the cotilting heart associated to a tilting complex is a locally coherent and locally coperfect Grothendieck category (i.e. an Ind-completion of a small artinian a…
Restricted injective dimensions over Cohen-Macaulay rings
Michal Hrbek, Giovanna Le Gros
We show that the small and large restricted injective dimensions coincide for Cohen-Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of Sath…
Fp-projective periodicity
Silvana Bazzoni, Michal Hrbek, Leonid Positselski
The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the behavior of the objects of cocycles in acyclic complexes. It is known that any flat $\mathsf{Proj…
Tilting complexes and codimension functions over commutative noetherian rings
Michal Hrbek, Tsutomu Nakamura, Jan Šťovíček
In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice"…
Topological endomorphism rings of tilting complexes
Michal Hrbek
In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that…
Silting, cosilting, and extensions of commutative ring
Simion Breaz, Michal Hrbek, George Ciprian Modoi
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the…
Singular equivalences to locally coherent hearts of commutative noetherian rings
Michal Hrbek, Sergio Pavon
We show that Krause's recollement exists for any locally coherent Grothendieck category such that its derived category is compactly generated. As a source of such categories, we co…
Gluing compactly generated t-structures over stalks of affine schemes
Michal Hrbek, Jiangsheng Hu, Rongmin Zhu
We show that compactly generated t-structures in the derived category of a commutative ring are in a bijection with certain families of compactly generated t-structures over th…
Parametrizing torsion pairs in derived categories
Lidia Angeleri Hügel, Michal Hrbek
We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-A) of a ring…
Telescope conjecture for homotopically smashing t-structures over commutative noetherian rings
Michal Hrbek, Tsutomu Nakamura
We show that any homotopically smashing t-structure in the derived category of a commutative noetherian ring is compactly generated. This generalizes the validity of the telescope…
Countably generated flat modules are quite flat
Michal Hrbek, Leonid Positselski, Alexander Slávik
We prove that if is a commutative Noetherian ring, then every countably generated flat -module is quite flat, i.e., a direct summand of a transfinite extension of localizati…
Definable coaisles over rings of weak global dimension at most one
Silvana Bazzoni, Michal Hrbek
In the setting of the unbounded derived category D(R) of a ring R of weak global dimension at most one we consider t-structures with a definable coaisle. The t-structures among the…
Compactly generated t-structures in the derived category of a commutative ring
Michal Hrbek
We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More…