相关论文: On $p$-adic limits of topological invariants

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…

We develop a theory of log adic spaces by combining the theories of adic spaces and log schemes, and study the Kummer \'etale and pro-Kummer \'etale topology for such spaces. We also establish the primitive comparison theorem in this…

In a paper of Tate and the author, we conjectured a uniform bound for the p-adic distance of torsion points on a semiabelian variety, not lying in a subvariety, to that subvariety. We survey the progress made on that conjecture and on…

In 2007, B. Poonen (unpublished) studied the $p$--adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bella\"iche asked the same question for the special case of Abelian varieties. These…

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…

We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…

In this work, we identify a certain family of higher-dimensional formal groups over the ring of $p$-adic integers such that any two formal groups in that class coincide if they share infinitely many torsion points. As a useful application,…

We determine the Haar measure on the compact $p$-adic special orthogonal groups of rotations $\mathrm{SO}(d)_p$ in dimension $d=2,3$, by exploiting the machinery of inverse limits of measure spaces, for every prime $p>2$. We characterise…

In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the…

The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…

We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of $p$-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes…

In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $\mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $\mathcal{L}$-operator acting on a space of harmonic cocycles on the…

Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main…

We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are obtained by gauging the symmetry of gapped, short-range…

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or $SU(N)$ connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the…

The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of…

Perfectoid spaces have become a crucial tool in $p$-adic geometry, serving as a bridge between adic spaces in characteristic $0$ and those in characteristic $p$. In this article, we develop a systematic way to study the structure of…

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem…

Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…

In this paper we consider the asymptotic behavior of invariants such as Betti numbers, minimal numbers of generators of singular homology, the order of the torsion subgroup of singular homology, and torsion invariants. We will show that all…