BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nivedita Bhaskar (University of Southern California) DTSTART:20200629T150000Z DTEND:20200629T160000Z DTSTAMP:20260513T204520Z UID:CMI/18 DESCRIPTION:Title: Bra uer p-dimensions of complete discretely valued fields\nby Nivedita Bha skar (University of Southern California) as part of CMI seminar series\n\n \nAbstract\n(This is joint work with Bastian Haase) To every central simpl e algebra A over a field F\, one can associate two numerical Brauer class invariants called the index(A) and the period(A). It is well known from th at index(A) divides high powers of per(A). The Brauer dimension of a field F is defined to be the least number n such that index(A) divides period(A )^n for every central simple algebra A defined over any finite extension o f F. Similarly there exist analogous notions of Brauer-p-dimensions of fie lds. The 'period-index' questions revolve around bounding the Brauer (p) d imensions of arbitrary fields.\n\nIn this talk\, we will look at the perio d-index question over complete discretely valued fields in the so-called ' bad characteristic' case (i.e when the residue field has characteristic p) . We will give a flavour of the known results for this question and discus s progress for the cases when the residue fields have small 'p-ranks'. Fin ally\, we will propose a (still open!) conjecture which very precisely rel ates the Brauer p-dimensions of the complete discretely valued fields to t he p-ranks of the residue fields\, along with some evidence via a family o f examples. The key idea involves working with Kato's filtrations and boun ding the symbol length of the second Milnor K group modulo p in a concrete manner\, which further relies on the machinery of differentials in charac teristic p as developed by Cartier.\n LOCATION:https://researchseminars.org/talk/CMI/18/ END:VEVENT END:VCALENDAR