Student Number Theory Seminar (Spring 2017)

The topic for this semester is Faltings's proof of the Mordell conjecture.

Organizers
David Hansen and Daniel Gulotta
Location and time
Thursdays at 10:10AM in 622 Math

References

Schedule of lectures

DateSpeakerTopicReferences
Jan 19Dan GulottaSpecial talk: Locally analytic distributions and the spectral haloPreprint
Jan 26David HansenOverview[CS] 1-2, [T1]
Feb 2Carl LianAbelian varieties[S] 2
Feb 9Dmitrii PirozhkovEndomorphisms of abelian varieties over finite fields[T1]
Feb 16Shizhang LiNéron models and reduction theorems[BLR] 1, [H] 4, [dJ]
Feb 23Qixiao MaTheory of heights[CS] 6, [D] 1, [M] 3-4, [H] 5
Mar 2Dan GulottaHodge-Tate decomposition for abelian varieties[M] 5, [F], [B], [T2]
Mar 9Sam Mundyp-divisible groups[M] 6, [T2], [CS] 3.3-3.6, [S] 4-5, 9
Mar 23Jingwei Xiaop-divisible groups[M] 6, [T2], [CS] 3.5-3.7, [S] 9-10
Mar 30Qixiao MaBehavior of Faltings height under isogeny[M] 7, [S] 20
Apr 6Faltings isogeny theorem[M] 8, [S] 20
Apr 13Raynaud's theorem on finite flat group schemes[M] 9
Shafarevich and Mordell conjectures[CS] 2.6, [S] 21-22

Possible additional topics: Siegel moduli schemes ([CS] 9, [H] 3), Arakelov intersection theory ([CS] 12), Hodge-Tate representations ([H] 9, [B])