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DTSTART:20181028T020000
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UID:calendar.67798.field_date.0@mathematics.huji.ac.il
DTSTAMP:20200606T120051Z
CREATED:20181106T060007Z
DESCRIPTION:Date: \n\n2:30pm to 3:30pm\n\n\n\n\nSee also: Number Theory &
Algebraic Geometry\, Events & Seminars\, SeminarsLocation: \n\nRoss 70\n
\n\n\nTitle: Tamagawa Numbers of Linear Algebraic Groups over Function Fie
lds Abstract: In 1981\, Sansuc obtained a formula for Tamagawa numbers of
reductive groups over number fields\, modulo some then unknown results on
the arithmetic of simply connected groups which have since been proven\, p
articularly Weil's conjecture on Tamagawa numbers over number fields. One
easily deduces that this same formula holds for all linear algebraic group
s over number fields. Sansuc's method still works to treat reductive group
s in the function field setting\, thanks to the recent resolution of Weil'
s conjecture in the function field setting by Lurie and Gaitsgory. However
\, due to the imperfection of function fields\, the reductive case is very
far from the general one\; indeed\, Sansuc's formula does not hold for al
l linear algebraic groups over function fields. We give a modification of
Sansuc's formula that recaptures it in the number field case and also give
s a correct answer for pseudo-reductive groups over function fields. The c
ommutative case (which is essential even for the general pseudo-reductive
case) is a corollary of a vast generalization of the Poitou-Tate nine-term
exact sequence\, from finite group schemes to arbitrary affine commutativ
e group schemes of finite type. Unfortunately\, there appears to be no sim
ple formula in general for Tamagawa numbers of linear algebraic groups ove
r function fields beyond the commutative and pseudo-reductive cases. Time
permitting\, we may discuss some examples of non-commutative unipotent gro
ups over function fields whose Tamagawa numbers (and relatedly\, Tate-Shaf
arevich sets) exhibit various types of pathological behavior.\n\n Export
\n \n\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20181112T143000
DTEND;TZID=Asia/Jerusalem:20181112T153000
LAST-MODIFIED:20181106T060007Z
SUMMARY:NT&AG: Zev Rosengarten
URL;TYPE=URI:https://mathematics.huji.ac.il/event/ntag-zev-rosengarten
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