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CALSCALE:GREGORIAN
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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:SPEAKER: Uriya First (University of Haifa)\n\nTITLE: "Generat
ion of algebras and versality of torsors" \n\nABSTRACT: The primitive elem
ent theorem states that every finite separable field extension L/K is gener
ated by a single element. An almost equally known folklore fact states that
every central simple algebra over a field can be generated by 2-elements.\
n\nI will discuss two recent works with Zinovy Reichstein (one is forthcomi
ng) where we establish global analogues of these results. In more detail\,
over a ring R (or a scheme X)\, separable field extensions and central simp
le algebras globalize to finite etale algebras and Azumaya algebras\, respe
ctively. We show that if R is of finite type over an infinite field K and h
as Krull dimension d\, then every finite etale R-algebra is generated by d+
1 elements and every Azumaya R-algebra of degree n is generated by 2+floor(
d/[n-1]) elements. The case d=0 recovers the well-known facts stated above.
Recent works of B. Williams\, A.K. Shukla and M. Ojanguren show that these
bounds are tight in the etale case and suggest that they should also be ti
ght in the Azumaya case.\n\nThe proof makes use of principal homogeneous G-
bundles T-->X (G is an affine algebraic group over K) which can specialize
to any principal homogeneous G-bundle over an affine K-variety of dimension
at most d. In particular\, such G-bundles exist for all G and d.\n\n______
________________________________________\n\nBjorn Poonen is inviting you to
a scheduled Zoom meeting.\n\nTopic: MIT number theory seminar\n\nTime: Apr
28\, 2020 04:30 PM Eastern Time (US and Canada)\n\n Every week on T
ue\, until May 5\, 2020\, 3 occurrence(s)\n\n Apr 28\, 2020 04:30 PM
\n\n May 5\, 2020 04:30 PM\n\nPlease download and import the followi
ng iCalendar (.ics) files to your calendar system.\n\nWeekly: https://mit.z
oom.us/meeting/tJUoc-6spjwuG9Ssez9bYJHWmT-BfkXuHB61/ics?icsToken=98tyKuCpqz
8tHtyStBiHRowcGY-gKOjxiGZbjfpujxr_WiJqSCvBO9YPELR0KM34\n\n \n\nJoin Zoom Me
eting\n\nhttps://mit.zoom.us/j/91547487410\n\n \n\nPassword: The order of t
he group S_5\n\n \n\nOne tap mobile\n\n+16465588656\,\,91547487410# US (New
York) 16699006833\,\,91547487410# US \n\n+(San Jose)\n\n \n\nMeeting ID: 9
15 4748 7410\n\nPassword: The order of the group S_5\n\n \n\nUS : +1 646 55
8 8656 or +1 669 900 6833\n\n \n\nInternational Numbers: https://mit.zoom.u
s/u/adhXbOf8mG\n\n \n\nJoin by SIP\n\n91547487410@zoomcrc.com\n\n \n\nJoin
by Skype for Business\n\nhttps://mit.zoom.us/skype/91547487410
DTEND:20200428T213000Z
DTSTAMP:20240911T232406Z
DTSTART:20200428T203000Z
GEO:42.358825;-71.090029
LOCATION:
SEQUENCE:0
SUMMARY:MIT Number Theory Seminar
UID:tag:localist.com\,2008:EventInstance_33315036998618
URL:https://calendar.mit.edu/event/mit_number_theory_seminar_9770
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