Related papers: Analytification of mapping stacks
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We study moduli spaces and moduli stacks for representations of associative algebras in Azumaya algebras, in rather general settings. We do not impose any stability condition and work over arbitrary ground rings, but restrict attention to…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
We construct shifted symplectic derived enhancements on rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension at least two. More generally, we prove that any $B\mathbb{G}_m$-action on a non-positively-shifted symplectic…
We develop the basic theory of derived quasi-coherent ideals for stacks relative to a given derived algebraic context. We compare different notions of adic completeness with respect to derived ideals, define and compare formal spectra and…
This is a survey paper on derived symplectic geometry, that will appear as a chapter contribution to the book "New Spaces for Mathematics and Physics", edited by Mathieu Anel and Gabriel Catren. Our goal is to explain how derived stacks can…
We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if…
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…
We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…
We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed…
In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective…
We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our previous works on the foundations of derived non-archimedean…
We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show…
This paper presents a survey on formal moduli problems. It starts with an introduction to pointed formal moduli problems and a sketch of proof of a Theorem (independently proven by Lurie and Pridham) which gives a precise mathematical…
In this survey we provide an overview of some recent developments in the construction of moduli spaces using stack-theoretic techniques. We will also explain the analogue of Harder-Narasimhan stratifications for general stacks, known as…
In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a…
We construct the \'etale motivic Borel-Moore homology of derived Artin stacks. Using a derived version of the intrinsic normal cone, we construct fundamental classes of quasi-smooth derived Artin stacks and demonstrate functoriality, base…
We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization…
We introduce a geometric completion of the stack of maps from stable marked curves to the quotient stack [point/GL(1)], and use it to construct some gauge-theoretic analogues of the Gromov-Witten invariants. We also indicate the…
We generalise the techniques of arXiv:0908.1963 to describe derived deformations in simplicial categories. This allows us to consider deformation problems with higher automorphisms, such as chain complexes (which have homotopies) and stacks…