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SUMMARY:Bruno Chiarellotto (Padoue)
DTSTART:20230127T093000Z
DTEND:20230127T103000Z
DTSTAMP:20260710T044238Z
UID:LAGA-AGAA/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGA-AGAA/67
 /">Multivariable de Rham representations\, Sen theory and $p$-adic differe
 ntial equations</a>\nby Bruno Chiarellotto (Padoue) as part of Séminaire 
 de géométrie arithmétique et motivique (Paris Nord)\n\nLecture held in 
 Salle B407\, bâtiment B\, LAGA\, Institut Galilée\, Université Paris 13
 .\n\nAbstract\nLet $K$ be a complete valued field extension of ${\\mathbb 
 Q}_p$ with perfect residue field. We consider $p$-adic representations of 
 a finite product $G^{\\Delta}_K$ of the absolute Galois group $G_K$ of $K$
 . This product appears as the fundamental group of a product of diamonds. 
 We develop the corresponding $p$-adic Hodge theory by constructing analogu
 es of the classical period rings ${\\mathbb B}_{\\rm dR}$ and ${\\mathbb B
 }_{\\rm HT}$\, and multivariable Sen theory. In particular\, we associate 
 to any $p$-adic representation $V$ of $G^{\\Delta}_K$ an integrable $p$-ad
 ic differential system in several variables ${\\mathbb D}_{\\rm dif }(V)$.
  We prove that this system is trivial if and only if the representation $V
 $ is de Rham. Finally\, we relate this differential system to the multivar
 iable overconvergent $(\\varphi\,\\Gamma)$-module of $V$ constructed by Pa
 l and Zabradi along classical Berger's construction. We will also deal wit
 h some new ideas on locally analytic vectors in this framework. Joint work
  with O. Brinon and N. Mazzari.\n
LOCATION:https://researchseminars.org/talk/LAGA-AGAA/67/
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