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SUMMARY:A functorial approach to the stability of vector bundles
DTSTART:20240410T130000Z
DTEND:20240410T140000Z
DTSTAMP:20240530T154300Z
UID:indico-event-269@events.dm.unipi.it
DESCRIPTION:Speakers: Dario Weissmann (Pisa)\n\nOn a smooth projective cur
ve the locus of stable bundles that remain stable on all etale Galois cov
ers prime to the characteristic defines a big open in the moduli space of
stable bundles. In particular\, the bundles trivialized on some etale Ga
lois cover of degree prime to the characteristic are not dense - in contr
ast to a theorem of Ducrohet and Mehta stating that all etale trivializab
le bundles are dense in positive characteristic. Etale trivializable bund
les correspond to representations of the etale fundamental group and we o
btain the upshot: the etale fundamental group behaves differently in posi
tive vs. characteristic 0.As an application we study the closure of the p
rime to p etale trivializable vector bundles. This closure is closely rel
ated to a stratification of the moduli space of stable vector bundles via
their decomposition behaviour on Galois covers of degree prime to the c
haracteristic. We obtain mostly sharp dimension estimates for the closure
of the prime to p etale trivializable bundles as well as the decompositi
on strata. \n\nhttps://events.dm.unipi.it/event/269/
LOCATION:Aula Seminari (Department of Mathematics)
URL:https://events.dm.unipi.it/event/269/
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