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SUMMARY:Peter Dillery (University of Maryland)
DTSTART:20240416T210000Z
DTEND:20240416T220000Z
DTSTAMP:20260423T010013Z
UID:UAANTS/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/86/">
 Comparing local Langlands correspondences</a>\nby Peter Dillery (Universit
 y of Maryland) as part of University of Arizona Algebra and Number Theory 
 Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nBroadly speaking\, for 
 G a connected reductive group over a local field F\, the Langlands program
  is the endeavor of relating Galois representations (more precisely\, "L-p
 arameters"---certain homomorphisms from the Weil-Deligne group of F to the
  dual group of G) to admissible smooth representations of G(F). There is c
 onjectured to be a finite-to-one map from irreducible smooth representatio
 ns of G(F) to L-parameters\, and there are many different approaches to pa
 rametrizing the fibers of such a map. \n\nThe goal of this talk is to expl
 ain some of these approaches\;  a special focus will be placed on the so-c
 alled "isocrystal" and "rigid" local Langlands correspondences. The former
  is best suited for building on the recent breakthroughs of Fargues-Scholz
 e\, while the latter is the broadest and is well-suited to endoscopy (a ve
 rsion of functoriality). We will discuss a proof of the equivalence of the
 se two approaches\, initiated by Kaletha for p-adic fields and extended to
  arbitrary nonarchimedean local fields in my recent work.\n
LOCATION:https://researchseminars.org/talk/UAANTS/86/
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