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SUMMARY:On Polynomial Ideals and Overconvergence in Tate Algebras
DTSTART;VALUE=DATE-TIME:20220630T090000Z
DTEND;VALUE=DATE-TIME:20220630T100000Z
DTSTAMP;VALUE=DATE-TIME:20220926T162600Z
UID:indico-event-8128@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tristan Vaccon (Université de Limoges)\n\nTate ser
ies are a generalization of polynomials introduced by John Tate in 1962\
, when defining a p-adic analogue of the correspondence between algebraic
geometry and analytic geometry. This p-adic analogue is called rigid geome
try\, and Tate series\, similar to analytic functions in the complex cas
e\, are its fundamental objects. Tate series are defined as multivariate
formal power series over a p-adic ring or field\, with a convergence cond
ition on a closed ball. The collection of such series forms a Tate algebra
.\n \n\nPolynomials are Tate series for any such convergence condition.\n
\nWe show that for an ideal in a Tate algebra generated by polynomials\, w
e can compute a Gröbner basis made of polynomials.\n\nThis generalize to
the case of an ideal in a Tate algebra generated by overconverging Tate se
ries\, i.e. Tate series converging on bigger balls.\n\n \n\nIn addition\,
we prove the existence of an analytic universal Gröbner basis for a poly
nomial ideal : a finite set of polynomial such that it is a Gröbner basis
for the completion of this ideal in any Tate algebra.\n\nThis is a joint
work with Xavier Caruso and Thibaut Verron.\n\nhttps://indico.math.cnrs.fr
/event/8128/
LOCATION:XR203 (XLIM)
URL:https://indico.math.cnrs.fr/event/8128/
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