WebWe present a construction of the derived moduli scheme of stable sheaves on Y , as a Geometric Invariant Theory quotient of the derived scheme of actions. The derived scheme of actions, RAct, was introduced by Ciocan-Fontanine and Kapranov in [3] as an auxiliary tool in their construction of the derived scheme of quotients, RQuot. WebIn chapter one, we explore the derived category of coherent sheaves on a variety through its group of autoequivalences. More precisely, we show that a scheme of finite type over a field is determined by its bounded derived category of coherent sheaves together with a collection of autoequivalences corresponding to an ample family of line bundles.

Non-commutative thickening of moduli spaces of stable sheaves

WebCalabi{Yau moduli schemes and moduli stacks Pantev et al. prove that if Y is a Calabi{Yau m-fold over K and M is a derived moduli scheme or stack of (complexes of) coherent sheaves on Y , then M has a natural (2 m)-shifted symplectic structure !. So Calabi{Yau 3-folds give 1-shifted derived schemes or stacks. WebOct 15, 2024 · The construction of the moduli space of stable sheaves using Berkovich analytic spaces will give rise to the non-archimedean version of Donaldson—Thomas invariants. In this paper we give the moduli construction over a non-archimedean field {\mathbb {K}}. We use the machinery of formal schemes, that is, we define and … raymond larmour lisburn

The derived moduli space of stable sheaves

WebOnce we can overcome this difficulty, the universality of the moduli space is easily derived from that of the Quot-scheme and the quotient. In the first section we shall recall a proof … WebExplicit examples of derived moduli problems addressed here are finite schemes, polarised projective schemes, torsors, coherent sheaves, and finite group schemes. Introduction In [Pri6], representability was established for many derived moduli problems involving schemes and quasi-coherent sheaves. However, the derived stacks there … WebIn algebraic geometry, a derived scheme is a pair (,) consisting of a topological space X and a sheaf either of simplicial commutative rings or of commutative ring spectra on X … raymond larmour