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SUMMARY:Pro-p Iwahori-Hecke modules and singularity categories - Nicolas D
 upre\, University of Wuppertal
DTSTART:20260304T163000Z
DTEND:20260304T173000Z
UID:TALK244714@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:Let G be the group of rational points of a p-adic reductive gr
 oup and H its associated pro-p Iwahori-Hecke algebra over a field k of cha
 racteristic p. The mod-p Langlands program aims to relate the representati
 on theory of G over k to that of the absolute Galois group of Q_p. The rep
 resentations of G in this context are however still very poorly understood
 . On the other hand\, the H-modules are much better understood and there e
 ven are results relating them to Galois representations. In earlier work\,
  we investigated the so-called Gorenstein projective model structure on th
 e category of H-modules and its associated homotopy category Ho(H). Assumi
 ng G has semisimple rank 1\, we will explain in this talk how this categor
 y Ho(H) identifies with the singularity category of a suitable scheme para
 metrising Galois representations\, building on earlier work of Pépin-Schm
 idt. After taking a suitable notion of support\, this recovers (most of) t
 he mod-p Langlands correspondence for GL_2(Q_p).
LOCATION:MR12
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