|Thursday, January 30 (lecture room K1)|
|09:00 - 09:10||Welcome and opening|
|09:10 - 10:00||Lidia Angeleri Hügel|
|10:30 - 11:20||Manuel Cortés Izurdiaga|
|11:30 - 12:20||George Ciprian Modoi|
|14:00 - 14:50||Xianhui Fu|
|15:30 - 16:20||Simion Breaz|
|16:30 - 17:20||Dolors Herbera|
|social dinner (from 19:30)|
|Friday, January 31 (lecture room K1)|
|10:00 - 10:50||Silvana Bazzoni|
|11:00 - 11:50||Sylvia Wiegand|
|12:20 - 13:10||Alberto Facchini|
|13:20 - 14:10||Mike Prest|
Enochs Conjecture (or Enochs question) asks if a class of modules providing for covers is necessarily closed under direct limits.
In a recent paper in collaboration with Leonid Positselski and Jan Šťovíček (http://arxiv.org/abs/1911.11720) it is shown that every direct limit presentation has locally split kernel (even quasi split) and this plays a key role in connection with precovers and covers. In particular, this allows to obtain a simple elementary proof of Enochs Conjecture for the left class of an n-tilting cotorsion pair in a Grothendieck category.
The paper deals also with covers and precovers of direct limits in AB3 categories, but in this talk I will mostly deal with module categories and I will discuss some classes of modules over commutative rings providing for minimal approximations, that is covers and/or envelopes.
In this talk we will focus on the problem of when, for a given Tor-pair (𝒯, 𝒮) in the categories of modules over a ring R, the class 𝒯 is closed under products or, more generally, products of modules in 𝒯 have finite projective dimension relative to 𝒯. As we will see, this property is related with some Mittag-Leffler conditions satisfied by the modules belonging to 𝒮. As a particular case of our results, we will obtain the characterization of those rings for which the class of all modules with finite flat dimension is closed under products.
This work is motivated by the study of right Gorenstein regular rings, that is, rings with finite right global Gorenstein projective dimension (equivalently, rings for which the classes of right modules with finite projective and with finite injective dimensions coincide).
In Geometry and Topology there are several functors between geometric spaces or topological spaces on the one hand, and commutative rings on the other. The most famous of these functors are probably the ring C(X) of real continuous functions of a topological space X and the spectrum Spec(R) of a commutative ring R. We will discuss the possibility of extending these classical ideas to the noncommutative setting. I will try to speak in a language understandable to everybody (i.e., to any mathematician...)
Let M be a finitely generated module, and let Addℵ0(M) denote the category of the direct summands of M(ω0). Let V*(M) denote the monoid of isomorphism classes of the objects in Addℵ0(M).
We will describe a process of "gluing" together the quotients of the category Addℵ0(M) by the ideal generated by an object of Addℵ0(M), to construct a submonoid B(M) of V*(M). What makes B(M) particularly interesting, is that in the case of a module finite algebra over commutative noetherian ring, B(M)=V*(M).
The particular way we found these monoids, motivated us to name them as monoids defined by a system of supports. We will develop some theory about them, mainly in the case of monoids defined by a full system of supports, which is the one appearing when R is a commutative local noetherian ring.
The talk is based on joint work with P. Příhoda and R. Wiegand.