Related papers: Syntomic complexes and $p$-adic \'etale Tate twist…

Here we present exact, stationary, parametric solutions to the Schr\"odinger--Poisson system. We confront two images: on one hand, we draw on the homotopy analysis method which leads us to a nonlinear integral scheme. Indeed, this approach…

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators \`a la Bernstein of the category of…

For every adic space $Z$ we construct a site $Z_t$, the tame site of $Z$. For a scheme $X$ over a base scheme $S$ we obtain a tame site by associating with $X/S$ an adic space $\textit{Spa}(X,S)$ and considering the tame site…

In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways , leading to a variety of symmetry enriched topological (SET) phases. While the symmetry…

We introduce $F$-gauges over a prism, construct syntomic cycle classes, and prove the prismatic Poincar\'e duality for proper smooth schemes.

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…

We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type $\mathfrak{a}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures. After setting up the general framework, we…

We will consider P-graph complexes, where P is a cyclic operad. P-graph complexes are natural generalizations of Kontsevich's graph complexes -- for P = the operad for associative algebras it is the complex of ribbon graphs, for P = the…

We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow categories of Morse-Smale functions $f$ to the setting where $f$ is equivariant under a finite group action and is Morse but no longer Morse-Smale.…

We make a systematic study of the infinitesimal lifting conditions of a pseudo finite type map of noetherian formal schemes. We recover the usual general properties in this context, and, more importantly, we uncover some new phenomena. We…

Let $p$ be a prime, and let $\mathrm{X}$ be a smooth $p$-adic formal scheme over $\mathrm{Spf} \mathcal{O}_K$ where $K/\mathbf{Q}_p$ is a finite extension. We show that reflexive sheaves on the stack $\mathrm{X}^{\mathrm{Syn}}$ are…

We construct log rigid syntomic cohomology for strictly semistable schemes over the ring of integers of a p-adic field, and prove that it is interpreted as the extension group of the complex of admissible filtered $(\phi,N)$-modules.

The Geometrical Lemma is a classical result in the theory of (complex) smooth representations of $p$-adic reductive groups, which helps to analyze the parabolic restriction of a parabolically induced representation by providing a filtration…

For a smooth affine group scheme $G$ over the ring of $p$-adic integers $\mathbb{Z}_p$ and a cocharacter $\mu$ of $G$, we study $G$-$\mu$-displays over the prismatic site of Bhatt-Scholze. In particular, we obtain several descent results…

In this paper, for any prime $p$, we propose the notion of a $p$-transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique trivial submodule to the case…

We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the…

We define smooth generalized crossed products and prove six-term exact sequences of Pimsner-Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the Quantum Heisenberg Manifolds in order to compute the…

The immediate snapshot complexes were introduced as combinatorial models for the protocol complexes in the context of theoretical distributed computing. In the previous work we have developed a formal language of witness structures in order…

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely…

The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract…