Moduli Space of Sheaves and Categorified Commutator of Functors

Yu, Zhiwen

doi:10.48550/arxiv.2112.12434

Cited by 1 publication

(2 citation statements)

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“…The study of Hecke correspondence in §8 is closely related to Negut ¸'s works [Ne17,Ne18,Ne19]; see also [PZ20,Z20,Z21].…”

Section: −−−−→ O ⊕3mentioning

confidence: 80%

“…Remark 8.3. This section's exposition and notations closely follow Negut ¸'s works [Ne17,Ne18,Ne19] which study the shuffle algebra structures and Hecke correspondences for the moduli of Gieseker stable sheaves on surfaces; see also [PZ20,Z21] for more results in this direction. We expect the results of this paper to be helpful for the study of similar algebraic structures for the general prestacks of perfect objects of Tor-amplitude [0, 1] on a surface X or a family X → S of surfaces.…”

Section: 34mentioning

confidence: 96%

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Derived projectivizations of complexes

Jiang¹

2022

Preprint

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In this paper, we study the counterpart of Grothendieck's projectivization construction in the context of derived algebraic geometry. Our main results are as follows: First, we define the derived projectivization of a connective complex, study its fundamental properties such as finiteness properties and functorial behaviors, and provide explicit descriptions of their relative cotangent complexes. We then focus on the derived projectivizations of complexes of perfect-amplitude contained in [0, 1]. In this case, we prove a generalized Serre's theorem, a derived version of Beilinson's relations, and establish semiorthogonal decompositions for their derived categories. Finally, we show that many moduli problems fit into the framework of derived projectivizations, such as moduli spaces that arise in Hecke correspondences. We apply our results to these situations. 7.1. The Fourier-Mukai functors and semiorthogonal decompositions 69 7.2. The local situation 72 7.3. Applications to classical examples 75 8. Hecke correspondence moduli as derived projectivizations 84 8.1. Hecke correspondences: the case of one-step flags 85 8.2. Hecke correspondences: the case of general flags 88 8.3. Hecke correspondences for surfaces 91 Appendix A. Simplicial Models for Symmetric and Koszul Algebras 95 A.1. Dold-Puppe and Quillen's construction 95 A.2. Simplicial symmetric algebras 95 A.3. Simplicial Koszul algebras 96 References 98

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“…The study of Hecke correspondence in §8 is closely related to Negut ¸'s works [Ne17,Ne18,Ne19]; see also [PZ20,Z20,Z21].…”

Section: −−−−→ O ⊕3mentioning

confidence: 80%