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SUMMARY:Daniel Kriz (MIT)
DTSTART:20201207T200000Z
DTEND:20201207T213000Z
DTSTAMP:20260422T220349Z
UID:STAGE/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/19/">D
 work's $p$-adic proof of rationality</a>\nby Daniel Kriz (MIT) as part of 
 STAGE\n\n\nAbstract\nIn 1959\, ex-electrical engineer Bernard Dwork shocke
 d the mathematical world by proving the first Weil conjecture on the ratio
 nality of the zeta function. Dwork's proof introduced striking new $p$-adi
 c methods\, and defied the expectation that the Weil conjectures could onl
 y be solved by developing a suitable Weil cohomology theory (later found t
 o be $l$-adic etale cohomology). In this talk we will outline Dwork's proo
 f and begin the initial part of the argument\, introducing Dwork's general
  notion of "splitting functions"\, the Artin-Hasse exponential and Dwork's
  lemma. \n\n\nReference: <a href="https://link.springer.com/book/10.1007/9
 78-1-4612-1112-9">Koblitz\, p-adic numbers\, p-adic analysis\, and zeta-fu
 nctions</a>\, pp. 92-95 and then Section V.2 to the end of the book\, some
  of which may be covered in a second lecture.\n
LOCATION:https://researchseminars.org/talk/STAGE/19/
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