Dmitrii Pirozhkov

activity

20182026

most citedStably semiorthogonally indecomposable varieties

8 citations · 9 across the 8 of their papers we have counts for

collaborators

9 papers

math.AG2026

On the support of admissible subcategories

Dmitrii Pirozhkov

Let $X$ be a smooth proper variety over an algebraically closed field of characteristic zero, and let $A \subset D_{coh}^{b} (X)$ be an admissible subcategory. Le…

math.AG2025

Generators vs. classical generators in derived categories of curves

Dmitrii Pirozhkov

This is mostly an expository note about an example communicated to the author by Aise Johan de Jong. In a triangulated category $T$ an object $G$ is said to be a classical generato…

math.AG2025

Admissible subcategories supported on curves

Dmitrii Pirozhkov

Let $X$ be a smooth projective variety. We study admissible subcategories of the bounded derived category of coherent sheaves on $X$ whose support is a proper subvariety $Z \subset…

math.AG2024

Towards homological projective duality for $Gr (2, 2 n)$

Dmitrii Pirozhkov

Consider a Grassmannian $Gr (2, V)$ for an even-dimensional vector space $V$ . Its derived category of coherent sheaves has a Lefschetz exceptional collection with respect t…

math.AG2022

Categorical Torelli theorem for hypersurfaces

Dmitrii Pirozhkov

Let $X \subset P^{n + 1}$ be a smooth Fano hypersurface of dimension $n$ and degree $d$ . The derived category of coherent sheaves on $X$ contains an interesting subcategory…

math.AG2020★ 8 cited

Stably semiorthogonally indecomposable varieties

Dmitrii Pirozhkov

A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonal…

math.AG2020★ 1 cited

Admissible subcategories of del Pezzo surfaces

Dmitrii Pirozhkov

We study admissible subcategories of derived categories of coherent sheaves on del Pezzo surfaces and rational elliptic surfaces. Using a relation between admissible subcategories…

math.AG2019

Rouquier dimension of some blow-ups

Dmitrii Pirozhkov

Raphaël Rouquier introduced an invariant of triangulated categories which is known as Rouquier dimension. Orlov conjectured that for any smooth quasi-projective variety $X$ the Rou…

math.AG2018

Semiorthogonal decompositions on total spaces of tautological bundles

Dmitrii Pirozhkov

Let U be the tautological subbundle on the Grassmannian $Gr (k, n)$ . There is a natural morphism $Tot (U) \to A^{n}$ . Using it, we give a semiorthogonal deco…

On the support of admissible subcategories

Generators vs. classical generators in derived categories of curves

Admissible subcategories supported on curves

Towards homological projective duality for Gr(2,2n)

Categorical Torelli theorem for hypersurfaces

Stably semiorthogonally indecomposable varieties

Admissible subcategories of del Pezzo surfaces

Rouquier dimension of some blow-ups

Semiorthogonal decompositions on total spaces of tautological bundles

Towards homological projective duality for $Gr (2, 2 n)$