Related papers: Non-locally modular regular types in classifiable …

Let $G$ be a locally compact group, and take $p\in(1,\infty)$. We prove that the Banach left $L^1(G)$-module $L^p(G)$ is injective (if and) only if the group $G$ is amenable. Our proof uses the notion of multi-norms. We also develop the…

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients…

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…

Let $p$ be a prime number, $G$ be a finite $p$-group and $K$ be a field of characteristic $p$. The Modular Isomorphism Problem (MIP) asks whether the group algebra $KG$ determines the group $G$. Dealing with MIP, we investigated a question…

In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order $p$ for a finite non-abelian $p$-group. We prove that if $G$ is a finite non-abelian $p$-group such that $G/Z(G)$ is powerful then…

Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…

The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…

Fix an odd prime $p$ and let $X$ be the $p$-localization of a finite suspended $CW$-complex. Given certain conditions on the reduced mod-$p$ homology $\bar H_*(X;\zmodp)$ of $X$, we use a decomposition of $\Omega\Sigma X$ due to the second…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

Let $X$ be a definable group definable over a small model $M_0$. Recall that a global type $p$ on $X$ is definable $f$-generic over $M_0$ if every left translate of $p$ is definable over $M_0$. We call $p$ strongly $f$-generic over $M_0$ if…

We generalize the main result of arXiv:1206.6631 [math.NT] to all totally real fields. In other words, for $p>2$ prime, we prove (under a mild Taylor-Wiles hypothesis) that if a modular representation is unramified and $p$-distinguished at…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

Let $X$ be an arbitrary set and let $T(X)$ denote the full transformation monoid on $X$. We prove that an element of $T(X)$ is unit-regular if and only if it is semi-balanced. For infinite $X$, we discuss regularity of the submonoid of…

Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We prove that the exponent and the abelianization of the centralizer of $G'$ in $G$ are determined by the group algebra of $G$ over any field…

We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…

We show that for every finite set of prime numbers S, there are at most finitely many singular moduli that are S-units. The key new ingredient is that for every prime number p, singular moduli are p-adically disperse. We prove analogous…

It is shown that each almost maximal valuation ring R such that every indecomposable injective module is countably generated, satisfies the following condition (C): each fp-injective module is locally injective. The converse holds if R is a…

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previous work of A. Kirillov, Jr. and V. Ostrik [Adv. Math. 171…

In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove (note…

We prove higher regularity for nonlinear nonlocal equations with possibly discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for corresponding local elliptic equations with VMO coefficients it is only possible to…