Related papers: Generic vanishing for semi-abelian varieties and i…
The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper we characterize the vanishing of such invariants for transversal unions of plane curves $C'$ and $C''$ in terms of the finiteness,…
We present an approach to Green-Lazarsfeld's generic vanishing combining gaussian maps and the Fourier-Mukai transform associated to the Poincar\`e line bundle. As an application we prove the Generic Vanishing Theorem for all normal…
We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or…
Let $f:\CN \rightarrow \C $ be a polynomial map, which is transversal at infinity. Using Sabbah's specialization complex, we give a new description of the Alexander modules of the hypersurface complement $\CN\setminus f^{-1}(0)$, and obtain…
We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…
We show that perverse equivalences between module categories of finite-dimensional algebras preserve rationality. As an application, we give a connection between some famous conjectures from the modular representation theory of finite…
A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…
We study the property of \emph{continuous Castelnuovo-Mumford regularity}, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in \cite{Kuronya:Mustopa:2020} by K\"{u}ronya and Mustopa. Our main result…
We show that some of the main results in Laurentiu Maxim's paper on this subject can be obtained (even in a slightly more general setting) using the theory of perverse sheaves of finite rank over $\Q$ as described for instance in the…
We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the…
This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…
We define and study twisted Alexander-type invariants of complex hypersurface complements. We investigate torsion properties for the twisted Alexander modules and extend classical local-to-global divisibility results to the twisted setting.…
For arbitrary field coefficients $\mathbb{K}$, we show that $\mathbb{K}$-perverse sheaves on a complex affine torus satisfy the so-called propagation package, i.e., the generic vanishing property and the signed Euler characteristic property…
We extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global…
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. This way, Durgun has introduced absolutely pure domains of modules as a mean…
In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--Lusztig characters when the parameters are generic. We…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
We classify the simple integrable modules of double affine Hecke algebras via perverse sheaves. We get also some estimate for the Jordan-Holder multiplicities of induced modules.
We first prove Bosch-L\"utkebohmert-Raynaud's conjectures on existence of global N\'eron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the…
Principal affine open subsets in affine schemes are an important tool in the foundations of algebraic geometry. Given a commutative ring $R$, $\,R$-modules built from the rings of functions on principal affine open subschemes in…