Related papers: Rigid non-cohomologically rigid local systems

We introduce a notion of rigid local system on the comple- ment of a plane curve $Y$, which relies on a canonical Waldhausen de- composition of the Milnor sphere associated to $Y$. We show that when $Y$ is weigthed homogeneous this notion…

We develop the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}^\mathrm{L})$. Among other things, we prove that every locally rigid commutative…

We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology…

Let $V$ be a finite relational vocabulary in which no symbol has arity greater than 2. Let $M$ be countable $V$-structure which is homogeneous, simple and 1-based. The first main result says that if $M$ is, in addition, primitive, then it…

We use a certain rigid local system in order to prove the potential automorphy of certain Galois representations with values in $G_2,$ found by N. Katz and the author.

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank,…

Let $(R,m)$ be a local Noetherian ring, let $I\subset R$ be any ideal and let $M$ be a finitely generated $R$-module. In 1990 Craig Huneke conjectured that the local cohomology modules $H^i_I(M)$ have finitely many associated primes for all…

We prove that the cohomology groups of an etale Q_p-local system on a smooth proper rigid analytic space are finite-dimensional Q_p-vector spaces, provided that the base field is either a finite extension of Q_p or an algebraically closed…

Let $A$ be a Dedekind domain of characteristic zero such that its localization at every maximal ideal has mixed characteristic with finite residue field. Let $R=A[X_1,\ldots, X_n]$ be a polynomial ring and $I=(a_1U_1, \ldots, a_c…

We construct elementary subgroups of all reductive groups of the local isotropic rank $\geq 2$ over rings and prove their basic properties. In particular, our results may be applied to the automorphism groups of any finitely generated…

When $p>2$, we construct a Hodge-type analogue of Rapoport-Zink spaces under the unramifiedness assumption, as formal schemes parametrising "deformations" (up to quasi-isogeny) of $p$-divisible groups with certain crystalline Tate tensors.…

A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability…

The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…

This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either…

This paper addresses two questions: (a) can we identify a sensible class of 2-parameter persistence modules on which the rank invariant is complete? (b) can we determine efficiently whether a given 2-parameter persistence module belongs to…

The number of equations needed to cut out a variety given by an ideal is called the arithmetic rank (of the ideal). It was shown in [8] that the notion of arithmetic rank is strongly related to the concept of regular sequences on the Matlis…

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L^\infty-eigenvalues. We make use of some…

A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.

Let $R$ be a complete regular local ring with an algebraically closed residue field and let $A$ be a Noetherian $R$-subalgebra of the polynomial ring $R[X]$. It has been shown in \cite{DO2} that if $\dim R=1$, then $A$ is necessarily…