BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:James Upton (UC San Diego)
DTSTART:20211202T220000Z
DTEND:20211202T230000Z
DTSTAMP:20260423T022814Z
UID:UCSD_NTS/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/48/
 ">Newton Polygons of Abelian $L$-Functions on Curves</a>\nby James Upton (
 UC San Diego) as part of UCSD number theory seminar\n\nLecture held in APM
  7321 and online.\n\nAbstract\nLet $X$ be a smooth\, affine\, geometricall
 y connected curve over a finite field of characteristic $p > 2$. Let $\\rh
 o:\\pi_1(X) \\to \\mathbb{C}^\\times$ be a character of finite order $p^n$
 . If $\\rho\\neq 1$\, then the Artin $L$-function $L(\\rho\,s)$ is a polyn
 omial\, and a theorem of Kramer-Miller states that its $p$-adic Newton pol
 ygon $\\mathrm{NP}(\\rho)$ is bounded below by a certain Hodge polygon $\\
 mathrm{HP}(\\rho)$ which is defined in terms of local monodromy invariants
 . In this talk we discuss the interaction between the polygons $\\mathrm{N
 P}(\\rho)$ and $\\mathrm{HP}(\\rho)$. Our main result states that if $X$ i
 s ordinary\, then $\\mathrm{NP}(\\rho)$ and $\\mathrm{HP}(\\rho)$ share a 
 vertex if and only if there is a corresponding vertex shared by certain "l
 ocal" Newton and Hodge polygons associated to each ramified point of $\\rh
 o$. As an application\, we give a local criterion that is necessary and su
 fficient for $\\mathrm{NP}(\\rho)$ and $\\mathrm{HP}(\\rho)$ to coincide. 
 This is joint work with Joe Kramer-Miller.\n\npre-talk at 1:20pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/48/
END:VEVENT
END:VCALENDAR