Related papers: Admissible local systems for a class of line arran…

Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-adic sheaves $_n{\cal K}_E$ on the moduli stack of rank $n$ vector bundles on $X$ with a section, which is…

Let $K$ be a field and let $R = K[X_1, \ldots, X_m]$ with $m \geq 2$. Give $R$ the standard grading. Let $I$ be a homogeneous ideal of height $g$. Assume $1 \leq g \leq m -1$. Suppose $H^i_I(R) \neq 0$ for some $i \geq 0$. We show (1)…

Let $M$ and $N$ be smooth (real or complex) manifolds, and let $M$ be equipped with some Riemannian metric. A continuous map $f\colon M\longrightarrow N$ admits a local $k$-multiplicity if, for every real number $\omega >0$, there exist $k$…

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…

Let $B$ be an arrangement of linear complex hyperplanes in $C^d$. Then a classical result by Orlik \& Solomon asserts that the cohomology algebra of the complement can be constructed from the combinatorial data that are given by the…

The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of the interest in these classifications is that it enables…

In the paper we prove Harbourne-Hirschowitz conjecture for quasi-homogeneous linear systems on $\mathbb P^2$ for $m=7$, 8, 9, 10, i.e. systems of curves of given degree passing through points in general position with multiplicities at least…

A shelf is a set with a binary operation~$\op$ satisfying $a \op (b \op c) = (a \op b) \op (a \op c)$. Racks are shelves with invertible translations $b \mapsto a \op b$; many of their aspects, including cohomological, are better understood…

We give two applications of the exponential Ax-Lindemann Theorem to local systems. One application is to show that for a connected topological space, the existence of a finite model of the real homotopy type implies linearity of the…

We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional…

This paper serves as a source of examples of Rokhlin actions or locally representable actions of finite groups on C*-algebras satisfying a certain UHF-absorption condition. We show that given any finite group $G$ and a separable, unital…

In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their completions, the number of different rulings, the number of…

Let A be a subspace arrangement with a geometric lattice such that codim(x) > 1 for every x in A. Using rational homotopy theory, we prove that the complement M(A) is rationally elliptic if and only if the sum of the orthogonal subspaces is…

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology…

Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$-irreducible, $G$-cohomologically rigid local system on $X$ with finite order abelianization and quasi-unipotent local monodromies…

Given a linear system in P^n with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear…

We count the number of countable homogeneous colored linear orderings in $k$ colors. Relatedly, we count the number of countable $C_{n,m}$-homogeneous linear orderings. $C_{n,m}$-homogeneity is a strong homogeneity notion that approximates…

This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative…

If the $\ell$-adic cohomology of a projective smooth variety, defined over a $\frak{p}$-adic field $K$ with finite residue field $k$, is supported in codimension $\ge 1$, then any model over the ring of integers of $K$ has a $k$-rational…