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DTSTAMP:20230918T214444
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SUMMARY:Presentation:A lower bound on the top degree rational cohomology of the symplectic group of a number ring
DESCRIPTION:Let R be a number ring. If one fixes i and lets n go to infinity\, then the rational cohomology H^i(SL_n(R)\; Q) stabilizes in a range.\nOutside this range\, little is known about the rational cohomology in general except that it vanishes for all i > \nu_n\, where \nu_n is an explicit constant described by Borel--Serre. For i=\nu_n\, Church--Farb--Putman recently showed that the dimension of H^{\nu_n}(SL_n(R)\; Q)$ is at least (|Cl(R)| -1)^{n-1}\, where Cl(R) denotes the class group of R. For the rational cohomology of the symplectic group Sp_{2n}(R)\, similar stability and vanishing patterns occur. In joint work with Benjamin Br\\"uck\, we obtain a similar lower bound for the the top degree rational cohomology of Sp_{2n}(R) and show it has dimension at least (|Cl(R)| -1)^n.
UID:112539-21829093@events.umich.edu
URL:https://events.umich.edu/event/112539
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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