[Todos CMAT] Seminario de Álgebra del IMERL - Lidia Angeleri-Hügel (Università degli Studi di Verona)

[seminarios en cmat.edu.uy]

Seminario de Álgebra del IMERL
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Título: "Wide coreflective subcategories and torsion pairs"

Expositor: Lidia Angeleri-Hügel (Università degli Studi di Verona)

Resumen:
 
A subcategory  X  of the module category Mod A over a ring A is said to be
reflective, respectively coreflective, if the inclusion functor X → Mod A admits
a left, respectively right, adjoint. A result of Gabriel and de la Peña
characterizes the subcategories which are both reflective and coreflective as
those which arise as module categories X = Mod B from some ring epimorphism A →
B. Much less is known when only one of the two conditions is satisfied, even
when restricting to wide, i.e. exact abelian, subcategories of Mod A.    In my
talk I will review a construction going back to work of Ingalls and Thomas which
assigns to a torsion pair two wide subcategories in Mod A. These subcategories
are often coreflective, and I will address the question of which wide
coreflective subcategories can be obtained in this way. When A is the Kronecker
algebra, this leads us to an open problem of Henning Krause and Greg Stevenson
concerning the classification of localizing subcategories in the derived
category of quasi-coherent sheaves on the projective line: are there more
localizing subcategories beyond the ones constructed from our understanding of
the compact objects?    The talk will be based on joint work with Francesco
Sentieri.
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Viernes 4/11 a las 11:15, A través de Zoom

Contacto: Marco A. Pérez - mperez en fing.edu.uy
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Zoom link for remote participants:

https://salavirtual-
udelar.zoom.us/j/85879414417?pwd=S3RqWHpuUXdGeHhucUNTa251Y1pZdz09   Meeting ID:
858 7941 4417  Passcode:   FGc=6*c en HV
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