An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...

Artin groups are a natural generalization of braid groups and are closely related to Coxeter groups in the following sense. There is a faithful representation of a Coxeter group W as a linear reflection group on a real vector space. The group acts properly and fixes a union of hyperplanes. The W-action extends as a covering space action to the complexified complement of these hyperplanes. The f...

In this paper, we show how the method introduced by Gaudry, Hess and Smart can be extended to a family of algebraic curves using Artin-Schreier extensions. This family also extends the number of hyperelliptic curves in characteristic 2 vulnarable to the Weil decent attack obtained by Galbraith. We also show that the genus of the resulting curve will be one of two easily computable values.

In this brief note, we prove the following two Artin-Schreier curves are supersin-gular.

We show that the smallest non-cyclic quotients of braid groups are symmetric groups, proving a conjecture Margalit. Moreover we recover results Artin and Lin about classification homomorphisms from on n strands to k letters, where is at most n. Unlike original proofs, our method does not use Bertrand-Chebyshev theorem, answering question Artin. Similarly for mapping class group closed orientabl...

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to spaces of semistable vector bundles. In the case of surfaces, we show (under a mild hypothesis on the twisting class) that the spaces are asympotically geometric...

In this sequel of [17, 18], we develop an adic formalism for étale cohomology of Artin stacks and prove several desired properties including the base change theorem. In addition, we define perverse t-structures on Artin stacks for general perversity, extending Gabber’s work on schemes. Our results generalize results of Laszlo and Olsson on adic formalism and middle perversity. We continue to wo...

In this paper we improve on Odlyzko’s lower bounds for the Artin conductor.