Related papers: Reciprocity obstruction to strong approximation ov…

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds, but a strong form of this theorem does not hold. Translating these…

We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant…

We study the homotopy theory of the classifying space of the complex projective linear groups to prove that purity fails for $PGL_p$-torsors on regular noetherian schemes when $p$ is a prime. Extending our previous work when $p=2$, we…

For a homogeneous space $G/H$ of reductive type, we consider the tangential homogeneous space $G_\theta/H_\theta$. In this paper, we give obstructions to the existence of compact Clifford-Klein forms for such tangential symmetric spaces and…

This article contains two rigidity type results for $\mathrm{SL}(n,\mathbb{Z})$ for large $n$ that share the same proof. Firstly, we prove that for every $p \in [1,\infty]$ different from $2$, the noncommutative $L^p$-space associated with…

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…

We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…

We prove weak type inequalities for a large class of noncommutative square functions. In conjunction with BMO type estimates, interpolation and duality, we will obtain the corresponding equivalences in the whole Lp scale. The main novelty…

We have tested four-point methods of the Hall effect measurement on BiSrCaCuO (2223) polycrystal and also the validity of the magnetic field form of the reciprocity theorem. We found that different types of determination of the Hall…

We present an obstruction theoretic inductive construction of intersection space pairs, which generalizes Banagl's construction of intersection spaces for arbitrary depth stratifications. We construct intersection space pairs for…

The authors study Hardy spaces, of arbitrary order, on a space of homogeneous type. This extends earlier work that treated only $H^p$ for $p$ near 1. Applications are given to the boundedness of certain singular integral operators,…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k satisfies the section conjecture. We prove many cases of…

The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces. We construct functors between the calculi from the…

We construct examples of smooth proper rigid-analytic varieties admitting formal model with projective special fiber and violating Hodge symmetry for cohomology in degrees $\geq 3$. This answers negatively a question raised by Hansen and…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel function. Moreover, smooth vector fields that are difficult…

Let \(\T\) be a commutative ternary \(\Gm\)-semiring in the sense of the triadic, \(\Gm\)-parametrized multiplication \(\{a,b,c\}_{\gamma}\). Building on the affine \(\Gm\)-spectrum \(\SpecG(\T)\), the structure sheaf, and the equivalence…

We determine the local equivalence class of the Seiberg-Witten Floer stable homotopy type of a spin rational homology 3-sphere $Y$ embedded into a spin rational homology $S^{1} \times S^{3}$ with a positive scalar curvature metric so that…

In this paper, we classify three-dimensional complex Abelian varieties isogenous to a product $A_1 \times A_2$, where one of the factors admits real multiplication by a real quadratic order $\mathcal{O}_D$ of discriminant $D$. We show that…