Smoothness of Derived Categories of Algebras

Autor: Alexey Elagin, Olaf M. Schnürer, Valery A. Lunts

Publikováno v: Moscow Mathematical Journal. 20:277-309

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: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1822a23ebe114d3bc7b007bf874395fa
https://doi.org/10.17323/1609-4514-2020-2-277-309

Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties

Autor: Daniel Bergh, Olaf M. Schnürer

Publikováno v: Bergh, D S T & Schnürer, O M 2021, ' Decompositions of derived categories of gerbes and of families of Brauer-Severi varieties ', Documenta Mathematica, vol. 26, pp. 1465-1500 . https://doi.org/10.25537/dm.2021v26.1465-1500
Documenta Mathematica

It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of complexes

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6903e55224154b5529b00d2b9f17bf8e

Conservative descent for semi-orthogonal decompositions

Autor: Daniel Bergh, Olaf M. Schnürer

Publikováno v: Bergh, D & Schnürer, O M 2020, ' Conservative descent for semi-orthogonal decompositions ', Advances in Mathematics, vol. 360, 106882 . https://doi.org/10.1016/j.aim.2019.106882
Advances in Mathematics

Motivated by the local flavor of several well-known semi-orthogonal decompositions in algebraic geometry, we introduce a technique called conservative descent, which shows that it is enough to establish these decompositions locally. The decomposition

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99c0c6643290b022c53fd1a68373f78e
http://arxiv.org/abs/1712.06845

Six operations on dg enhancements of derived categories of sheaves

Autor: Olaf M. Schnürer

We lift Grothendieck-Verdier-Spaltenstein's six functor formalism for derived categories of sheaves on ringed spaces over a field to differential graded enhancements. Our main tools come from enriched model category theory.
106 pages, small impr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::376be0be24ab707a2d560038dc843547
http://arxiv.org/abs/1507.08697

New enhancements of derived categories of coherent sheaves and applications

Autor: Olaf M. Schnürer, Valery A. Lunts

We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to functors between

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fcb1f2150c4dee1faa762c33d1804a9a
http://arxiv.org/abs/1406.7559