BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Uriya First (University of Haifa) DTSTART:20210628T150000Z DTEND:20210628T155000Z DTSTAMP:20260413T061129Z UID:zoomnovy/1 DESCRIPTION:Title: Generating algebras via versality\nby Uriya First (University of Haif a) as part of Algebraic groups and algebraic geometry: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nLet R be a noetherian (commutati ve) ring of Krull dimension d. A classical theorem of Forster states that a rank-n locally free R-module can be generated by n+d elements. Swan and Chase observed that this upper bound cannot be improved in general. I will discuss joint works with Zinovy Reichstein and Ben Williams where similar upper and lower bounds are obtained for R-algebras\, provided that R is o f finite type over an infinite field k. For example\, every Azumaya R-alge bra of degree n (i.e. an n-by-n matrix algebra bundle over Spec R) can be generated by floor(d/(n-1))+2 elements\, and there exist degree-n Azumaya algebras over d-dimensional rings which cannot be generated by fewer than floor(d/(2n-2))+2 elements. The case d=0 recovers the folklore fact that e very central simple algebra is generated by 2 elements over its center. Th e proof reinterprets the problem as a question on "how much versal" are ce rtain algebraic spaces approximating the classifying stack of the automorp hism scheme of the algebra in question.\n LOCATION:https://researchseminars.org/talk/zoomnovy/1/ END:VEVENT END:VCALENDAR