Related papers: Constant families of t-structures on derived categ…

Various topological properties of D-branes in the type--IIA theory are captured by the topologically twisted B-model, treating D-branes as objects in the bounded derived category of coherent sheaves on the compact part of the target space.…

It is usually not straightforward to work with the category of perverse sheaves on a variety using only its definition as a heart of a $t$-structure. In this paper, the category of perverse sheaves on a smooth toric variety with its orbit…

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \to S$. Given an admissible subcategory $\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…

The second author and Katzarkov introduced categorical invariants based on counting of full triangulated subcategories in a given triangulated category $\mathcal T$, and they demonstrated different choices of additional properties of the…

Let $S$ be a Noetherian scheme, and let $X$ be a scheme over $S$, such that all relative symmetric powers of $X$ over $S$ exist. Assume that either $S$ is of pure characteristic $0$ or $X$ is flat over $S$. Assume also that the structural…

For every stable model category $\mathcal{M}$ with a certain extra structure, we produce an associated model structure on the pro-category pro-$\mathcal{M}$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with…

We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a corollary, we identify the category of…

In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…

The moduli spaces of stable sheaves on projective schemes admit certain gluing data of Kapranov's NC structures, which we call quasi NC structures. The formal completion of the quasi NC structure at a closed point coincides with the…

Starting point of the present work is a conjecture of F. Catanese which says that in the derived category of coherent sheaves on any rational homogeneous manifold G/P there should exist a complete strong exceptional poset and a bijection of…

We apply the machinery of relative tensor triangular Chow groups to the action of the derived category of quasi-coherent sheaves on a noetherian scheme $X$ on the derived category of quasi-coherent $\mathcal{A}$-modules, where $\mathcal{A}$…

We prove the Gersten conjecture for $p$-adic \'etale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic \'etale Tate twists are not $\mathbb A^1$-invariant,…

We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…

In this paper we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug-Sosna and Addington for the universal ideal sheaf functor to be fully faithful…

Following the work of Beilinson, Bernstein and Deligne, we study restriction and induction of t-structures in triangulated categories with respect to recollements. For derived categories of piecewise hereditary algebras we give a necessary…

We classify bounded t-structures on the category of perfect complexes over a commutative, Noetherian ring of finite Krull dimension, extending a result of Alonso Tarrio, Jeremias Lopez and Saorin which covers the regular case. In…

We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…