相关论文: More on the lifting problem with the full ideal

A recent result of ours [GM] shows that all Hopf algebra liftings of a given diagram in the sense of Andruskiewitsch and Schneider are cocycle deformations of each other. Here we develop a "non-abelian" cohomology theory, which gives a…

The aim of this paper is to give natural examples of $\mathbf{\Sigma}_1^1$-complete and $\mathbf{\Pi}_1^1$-complete sets. In the first part, we consider ideals on $\omega$. In particular, we show that the Hindman ideal $\mathcal{H}$ is…

Let $F/\mathbb{Q}$ be any totally real number field and $\frak{N}$ an ideal of its ring of integers of norm $N$ and define, for every even $n$, the $[F:\mathbb{Q}]$-dimensional multiweight $\textbf{n}=(n,...,n)$. We prove that for a non CM…

Answering a question of Hru\v{s}\'ak, we show that every analytic tall ideal on $\omega$ contains an $F_\sigma$ tall ideal. We also give an example of an $F_\sigma$ tall ideal without a Borel selector.

We study the locus of the liftings of a homogeneous ideal $H$ in a polynomial ring over any field. We prove that this locus can be endowed with a structure of scheme $\mathrm L_H$ by applying the constructive methods of Gr\"obner bases, for…

If I is a suitably definable sigma-ideal on the real line and the factor algebra of Borel sets modulo I is weakly distributive then the algebra carries a Maharam submeasure.

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2^{|A|} = 2^{|B|}. This implies in particular that B has 2^{|B|} subalgebras. We also discuss…

For suitable groups G we will show that one can add a Boolean algebra B by forcing in such a way that Aut(B) is almost isomorphic to G. In particular, we will give a positive answer to the following question due to J.Roitman: Is…

For every integer $g \,\geq\, 2$ we show the existence of a compact Riemann surface $\Sigma$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${\mathcal O}^{\oplus 2}_{\Sigma}$ admits holomorphic connections with…

This paper proves a commutative algebraic extension of a generalized Skolem-Mahler-Lech theorem due to the first author. Let $A$ be a finitely generated commutative $K$-algebra over a field of characteristic $0$, and let $\sigma$ be a…

We show that the Nash-Williams theorem has a uniform version and that the Galvin theorem does not. We show that there is an $F_\sigma$ tall ideal on $\mathbb{N}$ without a Borel selector and also construct a $\mathbf\Pi^1_2$ tall ideal…

Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an elementary…

Among other results, we prove that if $I$ is a monomial ideal of $S=K[x_1,\ldots,x_n]$, where $K$ is a field, and $a\geq b-1\geq0$ are integers such that $a+b\leq\mathrm{proj~dim}(S/I)$, then $$t_{a+b}\leq…

A classical theorem of Micallef says that if $F \colon (\Sigma, g) \to \mathbb{R}^4$ is a stable minimal immersion of an oriented $2$-dimensional complete Riemannian manifold (that is parabolic) into $\mathbb{R}^4$, it is necessarily…

Let ${\mathbf U}_q^-$ be the negative part of the quantum enveloping algebra, and $\sigma$ the algebra automorphism on ${\mathbf U}_q^-$ induced from a diagram automorphism. Let $\underline{\mathbf U}_q^-$ be the quantum algebra obtained…

We study congruences involving $p$-adic families of Hecke eigensystems of Yoshida lifts associated with two Hida families (say $\mathcal{F},\mathcal{G}$) of elliptic cusp forms. With appropriate hypotheses, we show that if a Hida family of…

We study and classify topologically invariant $\sigma$-ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal…

We consider three lifting questions: Given a $C\sp{*}$-algebra $I$, if there is a unital $C\sp{*}$-algebra $A$ contains $I$ as an ideal, is every unitary from $A/I$ lifted to a unitary in $A$? is every unitary from $A/I$ lifted to an…

Each symmetrically-normed ideal $\mathcal{I}$ of compact operators on a Hilbert space $H$ induces a multiplier topology $\mu^*_{\mathcal{I}}$ on the algebra $\mathcal{B}(H)$ of bounded operators. We show that under fairly reasonable…

We show that there are models of MA where the boldface $\Sigma^1_3$-uniformization property holds. Further we show that BPFA and the assertion $\aleph_1$ is accessible to reals outright implies that the boldface $\Sigma^1_3$-uniformization…