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SUMMARY:Flatness properties of p-adic Banach modules - Andreas Bode\, Univ
 ersity of Cambridge
DTSTART:20161014T140000Z
DTEND:20161014T150000Z
UID:TALK67698@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:When studying normed modules over some Banach Q_p-algebra A\, 
 it is often necessary to replace the usual tensor product B ⊗_A M with i
 ts Banach completion B \\widehat{⊗}A M. We will investigate under which 
 conditions the functor B \\widehat{⊗}A − is exact\, or at least preser
 ves exactness for one given short exact sequence\, before generalizing our
  results to arbitrary chain complexes with finitely generated cohomology. 
 Flatness properties of B turn out to be closely linked to the notion of a 
 strict morphism\, and to torsion phenomena arising from the ‘unit ball t
 ensor’ B^o ⊗_(A^o) -. We also give applications in rigid analytic geom
 etry and the study of coadmissible \\wideparen{D}-modules.
LOCATION:CMS\, MR15
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