Friday, 6 June
01:15 pm
Bielefeld University B2-278
Tau-tilting theory and tau-tilting finiteness under scalar extension
Speaker: Erlend Borve
Seminar Representation Theory of Algebras
Let L:k be a field extension and let A be a finite-dimensional k-algebra. The extension of scalars of A along L:k is the L-algebra $A^L$, obtained by tensoring A and L over k. In the early 1980s, Jensen and Lenzing showed that extension of scalars preserves many module-theoretic and homological properties, particularly when L:k is MacLane separable. In particular, representation-finiteness is preserved in this case. However, if A is tau-tilting finte, i.e. it admits only a finite number of support tau-tilting modules up to isomorphism, this need not be true for $A^L$. We explore some examples and counter-examples of when tau-tilting finiteness is preserved. Along the way, we explain how tau-tilting theory and related notions lift under extension of scalars.\\ The talk is based on joint work in progress with Max Kaipel (Cologne).
02:30 pm
Bielefeld University B2-278
Characterizing higher Auslander(-Gorenstein) algebras
Speaker: Mohammad Hossein Keshavarz
Seminar Representation Theory of Algebras
It is well known that for Auslander algebras, the category of all (finitely generated) projective modules is an abelian category and this property of abelianness characterizes Auslander algebras by Tachikawa's theorem in 1974. Let n be a positive integer. In this talk, by using torsion theoretic methods, we show that n-Auslander algebras can be characterized by the abelianness of the category of modules with projective dimension less than n and a certain additional property, extending the classical Auslander-Tachikawa theorem. By Auslander-Iyama correspondence a categorical characterization of the class of Artin algebras having n-cluster tilting modules is obtained. Since higher Auslander algebras are a special case of higher Auslander-Gorenstein algebras, the results are given in the general setting as extending previous results of Kong. Moreover, as an application of some results, we give categorical descriptions for the semisimplicity and selfinjectivity of an Artin algebra. Higher Auslander-Gorenstein algebras are also studied from the viewpoint of cotorsion pairs and, as application, we show that they satisfy in two nice equivalences.
Next week
Wednesday, 11 June
02:15 pm
Bielefeld University V2-210/216
On Néron’s canonical local height functions for abelian varieties
Speaker: Robin de Jong
Algebraic and Arithmetic Geometry
We discuss Néron's canonical local heights on abelian varieties over non-archimedean valued fields from the point of view of Berkovich analytic spaces. We present a refinement of Néron's classical result relating his local heights with intersection multiplicities on the Néron model. Our result yields an extension to higher dimensions of Tate's explicit formulas for the canonical local heights on elliptic curves. This is based on joint work with Farbod Shokrieh.
03:45 pm
Bielefeld University V2-210/216
CM points and periods on products of non-Archimedean upper half-planes
Speaker: Carlos Caralps
Algebraic and Arithmetic Geometry
CM points over Shimura curves can be related to periods of a rigid analytic space using the theory of p-adic uniformization. In this talk, we will introduce the key points of this relationship and study a setting where the inverse process can be made explicit. More specifically, following the work of Bertolini, Darmon, and Green, we will show that some periods defined by integrals over products of non-Archimedean upper half-planes are related to CM points of Shimura curves.
Further Talks
Friday, 4 July
01:15 pm
Bielefeld University B2-278
tba
Speaker: Georgios Dalezios
Seminar Representation Theory of Algebras
01:15 pm
Bielefeld University B2-278
tba
Speaker: Martin Kalck
Seminar Representation Theory of Algebras