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SUMMARY:Rylan Gajek-Leonard (UMass Amherst)
DTSTART:20211112T200000Z
DTEND:20211112T210000Z
DTSTAMP:20260423T021421Z
UID:ANTULaval/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTULaval/7/
 ">Iwasawa Invariants of Modular Forms with $a_p=0$</a>\nby Rylan Gajek-Leo
 nard (UMass Amherst) as part of Algebra and Number Theory Seminars at Univ
 ersité Laval\n\n\nAbstract\nMazur-Tate elements provide a convenient meth
 od to study the analytic Iwasawa theory of $p$-nonordinary modular forms\,
  where the associated $p$-adic $L$-functions have unbounded coefficients. 
 The Iwasawa invariants of Mazur-Tate elements are well-understood in the c
 ase of weight 2 modular forms\, where they can be related to the growth of
  $p$-Selmer groups and decompositions of the $p$-adic $L$-function. At hig
 her weights\, less is known. By constructing certain lifts to the full Iwa
 sawa algebra\, we compute the Iwasawa invariants of Mazur-Tate elements fo
 r higher weight modular forms with $a_p=0$ in terms of the plus/minus inva
 riants of the $p$-adic $L$-function. Combined with results of Pollack-West
 on\, this forces a relation between the plus/minus invariants at weights 2
  and $p+1$.\n
LOCATION:https://researchseminars.org/talk/ANTULaval/7/
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