Derived categories of graded gentle one-cycle algebras

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules. This is applied to study derived categories of graded gentle one-cycle algebras.Comment: To appear in JPA

Spherical subcategories in algebraic geometry

We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general result is then applied to algebraic geometry.Comment: 21 pages. Identical to published version. There is a separate article with examples from representation theory, see arXiv:1502.0683

Spherical subcategories in representation theory

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.Comment: 36 pages, many changes to improve presentation, same content as published versio

Frobenius categories, Gorenstein algebras and rational surface singularities

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result to the Frobenius category of special Cohen-Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga-Gorenstein rings of finite GP type. We also apply our method to representation theory, obtaining Auslander-Solberg and Kong type results.Comment: 27 pages, to appear in Comp. Mat

Beyond the American Difficult Poem: Paul Celan’s “Du liegst”

This paper presents a close reading of a late poem by German poet Paul Celan, with a view to call into question several critical assumptions relating to modernist-derived “difficulty.” By looking in detail at what makes a poem “difficult” for the reader,a fact highlighted by a comparative approach, it becomes possible to move beyond such qualities as innovative, radical or avant-garde, and to consider what truly makes up our literary knowledge.Cet article propose une lecture détaillée d’un poème tardif de Paul Celan, de façon à remettre en question plusieurs présupposés critiques hérités du modernisme en matière de « difficulté ». En observant dans le détail ce qui rend un poème « difficile » pour le lecteur (phénomène que souligne l’approche comparatiste), il est plus aisé de se défaire d’une terminologie qui repose sur les notions d’innovation, de radicalité ou d’avant-garde, afin de comprendre où commence réellement notre savoir littéraire