BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Prashant Sridhar (TIFR\, Mumbai\, India) DTSTART:20210924T120000Z DTEND:20210924T130000Z DTSTAMP:20260423T021100Z UID:VCAS/101 DESCRIPTION:Title: F inding Maximal Cohen-Macaulay modules\nby Prashant Sridhar (TIFR\, Mum bai\, India) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n \nAbstract\nIn this talk\, we consider a problem that lies in the confluen ce of two topics.\nOn one hand\, we have maximal Cohen-Macaulay (MCM) modu les - these are classical objects that have been studied extensively from algebraic and geometric viewpoints. There is a rich theory of MCM modules over Cohen-Macaulay (CM) rings and many beautiful connections to the singu larities of the ring have been discovered. However\, in the absence of the CM property in the ring\, not as much is known - even the object's existe nce is largely unclear.\nOn the other hand\, we have a mixed characteristi c phenomenon. In 1980\, Paul Roberts showed that the integral closure of a regular local ring in an Abelian extension of its quotient field is CM\, provided the characteristic of the residue field does not divide the degre e of the extension. This fails in the "modular case" in mixed characterist ic.\nWe will look at some past results in the literature before considerin g the question of existence of MCMs in the modular case of Roberts's theor em.\n LOCATION:https://researchseminars.org/talk/VCAS/101/ END:VEVENT END:VCALENDAR