Dawid Kędzierski

• Phd
• assistant professor at University of Szczecin

In \cite{kk04} the second and third author extended the methods of \cite{pr} and determined the \tm module structure on $\Ext^1(\Phi,\Psi )$ where $\Phi $ and $\Psi$ were Anderson \tm modules over $A={\mathbf F}_q[t]$ of some specific types. This approach involved the concept of biderivation and certain reduction algorithm. In this paper we general...

In the work of M. A. Papanikolas and N. Ramachandran [A Weil-Barsotti formula for Drinfeld modules, Journal of Number Theory 98, (2003), 407-431] the Weil-Barsotti formula for the function field case concerning $\Ext_{\tau}^1(E,C)$ where $E$ is a Drinfeld module and $C$ is the Carlitz module was proved. We generalize this formula to the case where...

We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for deciding whether certain hyperfields cannot be obtained via Krasner’s quotient construction. We prov...

Abstract. Let A = Fq[t] be the polynomial ring over a finite field Fq and let φ and ψ be A−Drinfeld modules. In this paper we con- sider the group Ext^1(φ,ψ) with the Baer addition. We show that if rankφ > rankψ then Ext^1(φ,ψ) has the structure of a t−module. We give complete algorithm describing this structure. We generalize this to the cases: Ex...

In this article, we study modules over wild canonical algebras which correspond to extension bundles (Kussin et al. Adv Math 237:194–251, 2013) over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients related to the relations of the considered algebra. Moreover, we expa...

In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients related to the relations of the considered algebra. Moreover, we expand the concept of extension bundles over...

We show that ''almost all'' exceptional modules over wild canonical algebra $\Lambda$ can be described by matrices having coefficients $\lambda_i-\lambda_j$, where $\lambda_i, \lambda_j$ are elements from the parameter sequence. The proof is based on Schofield induction for sheaves in the associated categories of weighted projective lines and an ex...

Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the — suitably graded — triangle singularities f = x^a+y^b+ z^c of domestic type, that is, we assume that (a, b, c) are integers at least two, satisfying 1/a+ 1/b+ 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determin...

We show that each exceptional vector bundle on a weighted projective line in the sense of Geigle and Lenzing can be obtained by Schofield induction from exceptional sheaves of rank one and zero. This relates to results of Ringel concerning modules over finite dimensional k-algebras over an arbitrary field.