Related papers: Bertini theorems admitting base changes

Let $(T,\langle \cdot, \cdot, \cdot \rangle)$ be a Leibniz triple system of arbitrary dimension, over an arbitrary base field ${\mathbb F}$. A basis ${\mathcal B} = \{e_{i}\}_{i \in I}$ of $T$ is called multiplicative if for any $i,j,k \in…

It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that…

Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimension r and singular locus of dimension at most s, and let…

We prove that for a finite set of points $X$ in the projective $n$-space over any field, the Betti number $\beta_{n,n+1}$ of the coordinate ring of $X$ is non-zero if and only if $X$ lies on the union of two planes whose sum of dimension is…

Alternate bases are a numeration system that generalizes the R\'enyi numeration system. It is common in this context to construct examples or counter-examples by specifying the expansions of $1$ in the desired system. While it is easy to…

Let $u:A\to B$ be a morphism of noetherian local rings. We obtain smoothness criteria for algebras with differential bases, in the case of rings containing a field of characteristic $p>0.$ We also give smoothness criteria for reduced…

We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…

Neutrinos allow for a test of the hypothesis that the fermions of the Standard Model have Fermi-point splitting, analogous to the fermionic quasi-particles of certain condensed-matter systems. If present, the corresponding Lorentz-violating…

We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The result yields singular equivalences between rings of different…

We establish an Excision type theorem for niceness of group structure on the orbit space of unimodular rows of length $n$ modulo elementary action. This permits us to establish niceness for relative versions of results for the cases when $n…

We study the structure of a family of algebras which encodes a generalization of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to…

In this paper, we define a set of good basic invariants for a finite complex reflection group under certain conditions. We show that a set of good basic invariants for a finite real reflection group gives a set of the flat invariants…

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

We prove that the Betti numbers of simplicial complexes of bounded vertex degrees are testable in constant time.

We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…

We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…

We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…