BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Daniel Kriz (Università degli Studi di Milano)
DTSTART:20260603T150000Z
DTEND:20260603T160000Z
DTSTAMP:20260528T081419Z
UID:LNTS/195
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/195/">A
  canonical splitting of the p-adic Hodge filtration and applications</a>\n
 by Daniel Kriz (Università degli Studi di Milano) as part of London numbe
 r theory seminar\n\nLecture held in King's College London\, Strand campus\
 , Room S3.30.\n\nAbstract\nThe classical unit root splitting of the Hodge 
 filtration on universal p-adic de Rham cohomology over the ordinary locus 
 of Shimura varieties\, due to Dwork and Katz\, has had many applications i
 n the study of p-adic modular forms\, constructions of theta operators and
  Iwasawa theory. The well-known obstruction to extending this splitting in
 to the supersingular locus is the non-overconvergence of Katz's p-adic wei
 ght 2 Eisenstein series $E_2$. In this talk we discuss a new period sheaf 
 over which the Hodge filtration splits canonically\, containing periods wh
 ich can roughly be thought of as analytic continuations of $E_2$. Using th
 is sheaf\, we define a new theory of quasi-overconvergent modular forms an
 d p-adic Maass-Shimura operators acting on these forms\, which specialize 
 to Katz's p-adic modular forms and theta operators on the ordinary locus. 
 Using these operators\, we generalize and unify previous constructions due
  to the author and Andreatta-Iovita of p-adic L-functions of Katz- and BDP
 -type for p nonsplit in the CM field K\, defining a locally analytic p-adi
 c L-function on the full space of p-adic central critical characters which
  specializes on certain subdomains to each of these constructions. We will
  also discuss the arithmetic applications of these constructions\, includi
 ng generalizing the author's previous work on Iwasawa theory over K\, Sylv
 ester's conjecture on sums of rational cubes and Goldfeld's conjecture for
  the congruent number family.\n
LOCATION:https://researchseminars.org/talk/LNTS/195/
END:VEVENT
END:VCALENDAR