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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Featured Speaker : Elden Elmanto (Harvard University)\n\nOn t
he K-theory of Universal Homeomorphisms\n\nA universal homeomorphism of sch
emes is a morphism of schemes (frighteningly\, with no finiteness condition
s) which is a homeomorphism on underlying topological spaces (!) and remain
s so after arbitrary pullback. In some sense\, beginning with at least Grot
hendieck\, one should view a universal homeomorphism as analogous to the to
pologists notion of a weak equivalence. In this talk\, I will explain this
philosophy\, give examples\, and explain two re- sults about the behavior o
f algebraic K-theory under universal homeomorphisms. The first is an equich
aracteristic result: if k is a field of exponential characteristic c\, then
homotopy K-theory is invariant under universal homeomorphisms of k-schemes
\, after inverting c\; this is a consequence of joint work with Adeel Khan
and implies the statement for usual K-theory in positive characteristics. T
he second is a mixed characteristic result for usual (but p-inverted) K-the
ory: over Zp schemes\, universal homeomorphisms are completely controlled b
y its char- acteristic zero part. The formulation of the theorem\, and its
proof\, is inspired by some results in mixed characteristic birational geom
etry. This is joint work in progress with Akhil Mathew and Jakub Witaszek.
DTEND:20191007T213000Z
DTSTAMP:20210921T121133Z
DTSTART:20191007T203000Z
GEO:42.358262;-71.090045
LOCATION:Room : 2 - 131
SEQUENCE:0
SUMMARY:Algebraic Topology Seminar
UID:tag:localist.com\,2008:EventInstance_31450417480021
URL:https://calendar.mit.edu/event/algebraic_topology_seminar_20191007
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