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pro vyhledávání: '"Elagin, Alexey"'
Autor:
Elagin, Alexey
We continue the study of thick triangulated subcategories, started in arXiv:2007.02134, and consider thick subcategories in the derived category of a weighted projective curve and corresponding abelian thick subcategories. Our main result is that any
Externí odkaz:
http://arxiv.org/abs/2407.01207
We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation in the sense of L.Hille and M.Perling. We find simple geometric criteri
Externí odkaz:
http://arxiv.org/abs/2007.02140
Autor:
Elagin, Alexey, Lunts, Valery A.
We classify thick subcategories $\mathcal T \subset D^b(\mathrm{coh}\,C)$ for smooth projective curves $C$ over an algebraically closed field.
Comment: 20 pages. v2: acknowledgements added
Comment: 20 pages. v2: acknowledgements added
Externí odkaz:
http://arxiv.org/abs/2007.02134
Autor:
Elagin, Alexey
This is a companion paper of arXiv:1901.09461, where different notions of dimension for triangulated categories are discussed. Here we compute dimensions for some examples of triangulated categories and thus illustrate and motivate material from loc.
Externí odkaz:
http://arxiv.org/abs/2004.04694
Autor:
Elagin, Alexey, Lunts, Valery A.
Let $X_N$ be the second infinitesimal neighborhood of a closed point in $N$-dimensional affine space. In this note we study $D^b(coh\, X_N)$, the bounded derived category of coherent sheaves on $X_N$. We show that for $N\geq 2$ the lattice of triangu
Externí odkaz:
http://arxiv.org/abs/2002.06416
Autor:
Elagin, Alexey, Lunts, Valery A.
In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.
Comment: Comm
Comment: Comm
Externí odkaz:
http://arxiv.org/abs/1901.09461
We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for any algebra
Externí odkaz:
http://arxiv.org/abs/1810.07626
Autor:
Elagin, Alexey, Lunts, Valery A.
Publikováno v:
In Journal of Pure and Applied Algebra June 2022 226(6)
Autor:
Elagin, Alexey, Lunts, Valery
Publikováno v:
Sbornik: Mathematics, 209:12 (2018), 1756-1782
Let $R$ be a commutative Noetherian ring such that $X=Spec R$ is connected. We prove that the category $D^b(coh X)$ contains no proper full triangulated subcategories which are regular. We also bound from below the dimension of a regular category $T$
Externí odkaz:
http://arxiv.org/abs/1711.01492
We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling, while for
Externí odkaz:
http://arxiv.org/abs/1710.03972