online seminar, October 20 at 9am

[Martino Lupini]

Dear all,

In case anyone might be interested, I am giving an online talk on Monday morning at the Algebra & Topology Seminar organized by the University of Thessaloniki

Monday 20/10, 9-10 am (Italian time), 10-11 am (Greek time)
https://authgr.zoom.us/j/96179136945?pwd=dTRtbmtRbGlkaUhYSDhISXFmREhGQT09
Meeting ID: 961 7913 6945
Passcode: 640861

Please find below title and abstract

Best,

Martino

Phantom extensions of modules

In this talk, I will introduce the theory of phantom extensions of modules, recently developed in collaboration with Casarosa. The notion of phantom extension of order a given contable ordinal alpha produces a hierarchy of more and more stringent notions, where the case of alpha=0 corresponds to the classical notion of pure extension.  I will present several equivalent characterizations, the connection to phantom maps in topology, and the following Dichotomy Theorem: if C is a a flat module over a Dedekind domain, then either all extensions of C are trivial (which happens precisely when C is divisible), or C admits nontrivial phantom extensions of order alpha for any countable ordinal alpha.