Publications (11)
A categorical characterization of quantum projective -spaces
Izuru Mori, Adam Nyman
In this paper, we study a generalization of the notion of AS-regularity for connected -algebras. Our main result is a characterization of those categories equivalent to…
Local duality for connected Z-algebras
Izuru Mori, Adam Nyman
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of…
The geometry of points on quantum projectivizations
Adam Nyman
Suppose is an affine, noetherian scheme, is a separated, noetherian -scheme, is a coherent -bimodule and $\mathcal{I} \subset T(\mathcal…
Non-commutative Mori contractions and $\PP^1$-bundles
Daniel Chan, Adam Nyman
We give a method for constructing maps from a non-commutative scheme to a commutative projective curve. With the aid of Artin-Zhang's abstract Hilbert schemes, this is used to cons…
Noncommutative linear systems and noncommutative elliptic curves
Daniel Chan, Adam Nyman
In this paper we introduce a noncommutative analogue of the notion of linear system, which we call a helix in an a…
Three-periodic helices on elliptic curves and their associated regular algebras
Daniel Chan, Adam Nyman
Let denote an algebraically closed field of characteristic zero and let denote a smooth elliptic curve over . Given a three-periodic elliptic helix $\underline{\mathcal{…
Two-periodic elliptic helices: classification and geometry
Daniel Chan, Adam Nyman
Let denote an algebraically closed field of characteristic zero and let denote a smooth elliptic curve over . In this paper, motivated by work in \cite{CN}, we think of…
The Eilenberg-Watts theorem over schemes
Adam Nyman
We study obstructions to a direct limit preserving right exact functor between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. Wh…
A structure theorem for P^1-Spec k-bimodules
Adam Nyman
Let k be an algebraically closed field. Using the Eilenberg-Watts theorem over schemes, we determine the structure of k-linear right exact direct limit and coherence preserving fun…
A representation theoretic study of noncommutative symmetric algebras
Daniel Chan, Adam Nyman
We study Van den Bergh's noncommutative symmetric algebra (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}…
The geometry of arithmetic noncommutative projective lines
Adam Nyman
Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space equal to the projectivization of the no…