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Algébricité, Groupes Formels de Lubin-Tate Et Modules de Drinfeld by Cadic-C

Algébricité, Groupes Formels de Lubin-Tate Et Modules de Drinfeld

by Cadic-C
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Book cover type: Paperback
  • ISBN13: 9786131517853
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 128
  • Original Price: GBP 41.0
  • Language: French
  • Edition: N/A
  • Item Weight: 200 grams
  • BISAC Subject(s): Algebra / General

Ce travail part de l''observation d''un résultat de P. Robba établi en 1982 dont l''énoncé est le suivant: si k est un entier p-adique, alors la série (1+T) k mod p de Fp[[T]] est algébrique sur Fp(T) si et seulement si k est rationnel. En remarquant que cette série a une expression très proche de celle d''un endomorphisme du groupe multiplicatif sur l''anneau des entiers p-adiques, nous généralisons ce résultat à une classe de groupes formels de Lubin-Tate. Nous interprétons ensuite ce résultat via le foncteur de Fontaine et Wintenberger et en tirons des conséquences sur l''indépendance algébrique des automorphismes de corps locaux. Dans la deuxième partie de ce travail, nous établissons l''analogue du théorème de P. Robba dans le cas des modules de Drinfeld de rang 1 définis sur le complété P-adique de Fq[t] où P est un polynôme irréductible, unitaire et à coefficients dans le corps fini Fq.

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