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SUMMARY:Effective and minimal cones of weights for Hilbert modular forms (
 joint with P. Kassaei) - Fred Diamond (KCL)
DTSTART:20250603T120000Z
DTEND:20250603T130000Z
UID:TALK230917@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:I’ll discuss some generalizations of the well-known fact tha
 t there are non non-zero modular forms of negative weight\, even when work
 ing in characteristic p.   In particular\, for Hilbert modular forms assoc
 iated to a totally real field of degree d\, the weight is a d-tuple\, all 
 components of which are non-negative\, if working in characteristic zero. 
  But there are mod p Hilbert modular forms\, called partial Hasse invarian
 ts\, whose weight in some component is negative.  I’ll explain joint wor
 k with Kassaei (from 2017/2020) that shows the possible weights of non-zer
 o Hilbert modular forms in characteristic p lie in the cone generated by t
 he weights of these partial Hasse invariants.   In fact we prove a stronge
 r result (motivated by the relation with Galois representations) which ass
 erts that any form whose weight lies outside a certain minimal cone is div
 isible by a partial Hasse invariant.  I’ll also discuss a recent general
 ization of these results to forms on Goren-Oort strata of Hilbert modular 
 varieties.
LOCATION:MR12
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