Commutative Algebra Seminar
Fall 2026
Regular Day: Friday
Regular Time: 2:00PM - 3:00PM
Regular Location: LCB 222
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August 28 |
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September 4 |
Srikanth Iyengar
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September 11 |
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September 18 |
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September 25 |
Alex Scheffelin
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To a triple of a ring $R$, an $R$-module $M$, and an ideal $I$ we can associate the local cohomology
modules $H^n_I(M)$. One classical problem dating back to a question of Grothendieck is to identify when these vanish
for all $n i$ and all modules $M$, the smallest such $i$ we denote the cohomological dimension of $R$ with respect
to $I$. Grothendieck showed that this is bounded by $d = \dim R$, while a very simple condition on $\widehat{R}$ and
$I\widehat{R}$ controls the vanishing at $d$. A more subtle topological condition controls the vanishing at $d-1$
for regular local rings as posed by Hartshorne in the late 60s, and was proven in equicharacteristic in the early
70s. After 50 years it was shown to be true in unramified mixed characteristic, and the main result of this talk is
the ramified mixed characteristic case.
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October 2 |
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October 9 |
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October 16 |
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October 23 |
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October 30 |
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November 6 |
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November 13 |
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November 20 |
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November 27 |
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December 4 |
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