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Flatness properties of p-adic Banach modules

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  • UserAndreas Bode, University of Cambridge
  • ClockFriday 14 October 2016, 15:00-16:00
  • HouseCMS, MR15.

If you have a question about this talk, please contact Nicolas Dupré .

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 its Banach completion B \widehat{⊗}A M. We will investigate under which conditions the functor B \widehat{⊗}A − is exact, or at least preserves 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 tensor’ Bo ⊗_(Ao) -. We also give applications in rigid analytic geometry and the study of coadmissible \wideparen{D}-modules.

This talk is part of the Junior Algebra and Number Theory seminar series.

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