Related papers: Generalizing the GAGA Principle

We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…

Using the theory of $(\varphi, \Gamma)$-modules we generalizes Greenberg's construction of the $\Cal L$-invariant to semistable representations

We show that the compactification of the moduli space of $n-$nodal curves of genus g, i.e. $\mathcal{N}_{g,n}:= \mathcal{M}_{g,2n} /G$, with $G:=(\mathbb{Z}_2)^n \rtimes S_n$, is of general type for $g \geq 24$, for all $n \in \mathbb{N}$.…

In this paper we study generic M(atrix) theory compactifications that are specified by a set of quotient conditions. A procedure is proposed, which both associates an algebra to each compactification and leads deductively to general…

This is the third paper in a series, following [FPVa] and [FPVb]. We classify all modular compactifications of the universal Jacobian over $\overline{\mathcal{M}}_{g,n}$, both as stacks and as their relative good moduli spaces. Our main…

In a previous paper we have constructed a compactification $KGl_n$ of the general linear group $Gl_n$, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De…

In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the $M$ theory on noncommutative tori. This…

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields, such as (i) G is definably an almost direct product of a semisimple group and a commutative group, and (ii) the group (G, .) is…

In this paper, we study all ways of constructing modular compactifications of the moduli space $\mathcal{M}_{g,n}$ of $n$-pointed smooth algebraic curves of genus $g$ by allowing markings to collide. We find that for any such…

We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Grauert's theorem for derived direct images under proper…

In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme…

We prove formal GAGA for good moduli space morphisms under an assumption of "enough vector bundles" (which holds for instance for quotient stacks). This supports the philosophy that though they are non-separated, good moduli space morphisms…

Let $X$ be an algebraic variety over $\mathbf{C}$. We define a canonical compactification $X^{\!\urcorner}$ of the complex analytic space $X(\mathbf{C})$ by adding a Berkovich space over a trivially valued field at the boundary. The…

We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure $M$ is cellular if and only if $M$ is $\omega$-categorical and mutually algebraic. Second,…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…

We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a…

We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…

We construct a compactification of the universal moduli space of semistable principal $G$-bundles over $\overline{\textrm{M}}_{g}$, the fibers of which over singular curves are the moduli spaces of $\delta$-semistable singular principal…

For a stable curve of genus $g\geq 2$ and simple Lie algebra of type A or C, we show that the conformal blocks algebra $\mathcal{A}$ on $\overline{\mathcal{M}}_g$ is finitely generated and establish an explicit connection to Schmitt and…