Related papers: Derived Non-archimedean analytic Hilbert space

Most of results of Bestvina and Mogilski [\textit{Characterizing certain incomplete infinite-dimensional absolute retracts}, Michigan Math. J. \textbf{33} (1986), 291--313] on strong $Z$-sets in ANR's and absorbing sets is generalized to…

Let \pi : X -> S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack, the Hilbert stack, parameterizing proper algebraic stacks mapping quasi-finitely…

Let $f: X \to \mathbb{A}^1$ be a regular function on a smooth complex algebraic variety $X$. We formulate and prove an equivalence between the algebraic formal twisted de Rham complex of $f$ and the vanishing cycles with respect to $f$ as…

Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we…

In this article we continue our investigation of the Derived Equivalences over noetherian quasi-projective schemes $X$, over affine schemes $\spec{A}$. For integers $k\geq 0$, let $C{\mathbb M}^k(X)$ denote the category of coherent…

Let $k$ be a field. In this paper, we define the notion of semi-fiber products of commutative $k$-algebras and show that the class of such rings contains several classes of commutative rings, including that of the fiber products of local…

We prove that the category of dg-modules and dg-algebras in a Grothendieck quasi-abelian category are endowed with a Quillen model structure. This allows some flexibility in setting up a theory of derived algebraic geometry in the infinite…

In equivariant geometry, a localization (a.k.a., concentration) theorem is typically interpreted as a relationship between the equivariant geometry of a space with a group action and the geometry of its fixed locus. We take a different…

In this paper we study certain sheaves of $p$-adically complete rings of differential operators on semistable models of the projective line over the ring of integers in a finite extension $L$ of ${\mathbb Q}_p$. The global sections of these…

We investigate algebraicity properties of quotients of complex spaces by complex reductive Lie groups G. We obtain a projectivity result for compact momentum map quotients of algebraic G-varieties. Furthermore, we prove equivariant versions…

We introduce smooth L^\infty differential forms on a singular (semialgebraic) set X in R^n. Roughly speaking, a smooth L^\infty differential form is a certain class of equivalence of 'stratified forms', that is, a collection of smooth forms…

This article establishes, for an appropriate localisation of associative rings, a long exact sequence in algebraic K-theory. The main result goes as follows. Let A be an associative ring and let A-->B be the localisation with respect to a…

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family $H_s$ of Hilbert spaces, and the question arises if the spaces $H_s$ are canonically isomorphic. [ADW] and…

Let $k[x]_{(x)}$ be the polynomial ring $k[x]$ localized in the maximal ideal $(x)\subseteq k[x]$. We study the Hilbert functor parameterizing ideals of colength $n$ in this ring {\it having support at the origin}. The main result of this…

We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincar\'e $\infty$-category, with no assumptions on the invertibility of $2$. Along…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

It is well known that related with the irreducible representations of the Lie group $SO(2)$ we find a discrete basis as well a continuous one. In this paper we revisited this situation under the light of Rigged Hilbert spaces, which are the…

We observe that for a large class of non-amenable groups $G$, one can find bounded representations of $A(G)$ on Hilbert space which are not completely bounded. We also consider restriction algebras obtained from $A(G)$, equipped with the…

We prove a finiteness theorem and a comparison theorem in the theory of \'etale cohomology of rigid analytic varieties. By a result of Huber, for a quasi-compact separated morphism of rigid analytic varieties with target being of dimension…

For a recollement of derived module categories of rings, we provide sufficient conditions to guarantee the additivity formula of higher algebraic K-groups of the rings involved, and establish a long Mayer-Vietoris exact sequence of higher…