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UID:news742@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190211T221148
DTSTART;TZID=Europe/Zurich:20130412T103000
SUMMARY:Seminar Algebra and Geometry: Antoine Ducros (Université Paris 6)
DESCRIPTION:If one tries to mimic naively in the  p-adic setting what is u
 sually done in complex analytic geometry\, one immediately faces big probl
 ems\, because p-adic fields are totally disconnected. Hence in order to de
 velop a relevant p-adic geometry\, a more subtle approach is needed.    In
  this talk\, I will begin with a presentation of that of Berkovich. It   r
 oughly consists of 'adding plenty of points' to the usual p-adic  spaces s
 o that they get good topological properties (like  local  path-connectedne
 ss). I will describe some Berkovich spaces  associated  with simple variet
 ies (the projective line\, the algebraic  curves....).   \\r\\nThen I will
  try to illustrate the following slogan: 'to see the good analog of a comp
 lex object in the p-adic  world\, one often has to work with Berkovich spa
 ces'\,  through three  examples: spectral theory\; dynamical systems\; and
  the  theory of real  (p\,q)-forms and related notions (integrals\, bounda
 ry  integrals\,  curvature forms of metrized line bundles) that  as been r
 ecently  developped in the framework of Berkovich spaces by  Chambert-Loir
  and  myself\, and that I will try to describe in some  detail.
X-ALT-DESC:If one tries to mimic naively in the&nbsp\; <i>p-</i>adic settin
 g what is usually done in complex analytic geometry\, one immediately face
 s big problems\, because <i>p</i>-adic fields are totally disconnected. He
 nce in order to develop a relevant <i>p-</i>adic geometry\, a more subtle 
 approach is needed. <br /> <br />  In this talk\, I will begin with a pres
 entation of that of Berkovich. It   roughly consists of 'adding plenty of 
 points' to the usual <i>p</i>-adic  spaces so that they get good topologic
 al properties (like  local  path-connectedness). I will describe some Berk
 ovich spaces  associated  with simple varieties (the projective line\, the
  algebraic  curves....). <br />  \nThen I will try to illustrate the follo
 wing slogan: 'to see the good analog of a complex object in the <i>p</i>-a
 dic  world\, one often has to work with Berkovich spaces'\,  through three
   examples: spectral theory\; dynamical systems\; and the  theory of real 
  (p\,q)-forms and related notions (integrals\, boundary  integrals\,  curv
 ature forms of metrized line bundles) that  as been recently  developped i
 n the framework of Berkovich spaces by  Chambert-Loir and  myself\, and th
 at I will try to describe in some  detail. 
DTEND;TZID=Europe/Zurich:20130412T120000
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