Related papers: Formal models for relative adic spaces

We consider the 1D cubic NLS on $\mathbb R$ and prove a blow-up result for functions that are of borderline regularity, i.e. $H^s$ for any $s<-\frac 12$ for the Sobolev scale and $\mathcal F L^\infty$ for the Fourier-Lebesgue scale. This is…

We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of an elliptic…

We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent…

Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse…

We develop the formal theory of monads, as established by Street, in univalent foundations. This allows us to formally reason about various kinds of monads on the right level of abstraction. In particular, we define the bicategory of monads…

We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of etale Zp-local systems and etale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more…

Traditional category theory is typically based on set-theoretic principles and ideas, which are often non-constructive. An alternative approach to formalizing category theory is to use E-category theory, where hom sets become setoids. Our…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

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,…

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to ${\sf Q}$-categories by Kostanek and Waszkiewicz. This paper concerns the influence of the structure of the quantale ${\sf Q}$ on the…

In this work, I address a primary issue with adapting categorical and algebraic concepts to functional analytic settings, the lack of free objects. Using a "normed set" and associated categories, I describe constructions of normed objects,…

We provide a complete system of analytic invariants for unfoldings of non-linearizable resonant complex analytic diffeomorphisms as well as its geometrical interpretation. In order to fulfill this goal we develop an extension of the Fatou…

We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present some results and examples and conclude our paper with a…

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…

We consider a class of tachyon-like potentials, inspired by string theory, D-brane dynamics and cosmology in the context of classical and quantum mechanics. Motivated by the trans-Plankcian problem in the very early stage of cosmological…

We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we…

Recently Atobe-Oi-Yasuda established the newform theory for irreducible tempered generic representations of unramified ${\rm U}_{2n+1}$ over non-archimedean local fields. In this paper we extend their result to every irreducible generic…

In arXiv:0805.0157v5, the authors define a class of derived stacks, called "perfect stacks" and show that for this class the categories of quasi-coherent sheaves satisfy a categorical K\"unneth formula. Motivated to extend their results to…