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SUMMARY:Rahul Gupta
DTSTART:20230503T140000Z
DTEND:20230503T150000Z
DTSTAMP:20260422T104807Z
UID:FGC-IPM/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/34/"
 >Tame class field theory</a>\nby Rahul Gupta as part of FGC-HRI-IPM Number
  Theory Webinars\n\n\nAbstract\nAs a part of global class field theory\, w
 e construct a reciprocity map that describes the unramified (resp. tame) 
 étale fundamental group as a pro-completion of a suitable idele class gro
 up (resp. tame idele class group) for smooth curves over finite fields. Th
 ese results were extended to higher-dimensional smooth varieties over fini
 te fields by Kato-Saito (unramified case\, in 1986) and\nSchmidt-Spiess (t
 ame case\, in 2000). We begin the talk by recalling these results.\n\nThe 
 main focus of the talk is to work with smooth varieties over local fields.
  The class field theory over local fields is not as nice as that over fini
 te fields. We discuss results in the unramified class field theory over lo
 cal fields achieved in the period 1981--2015 by various mathematicians (Bl
 och\, Saito\, Jennsen\, Forre\, etc.). We then move to the main topic of t
 he talk which is the tame class field theory over local fields and prove t
 hat the results in the tame case are similar to that in the case of unrami
 fied class field theory.\n\nThis talk will be based on a joint work with A
 . Krishna and J. Rathore.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 5139
 92\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/34/
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