On Spectral Sequences for Iwasawa Adjoints à la Jannsen for Families

       Autors: Oliver Thomas and Otmar Venjakob
       Titel:  On Spectral Sequences for Iwasawa Adjoints à la Jannsen for Families
       Jahr: 2017
       Seiten: 22
       In: preprint
     

      
      Abstract: In \citenospec{MR1097615} several spectral sequences for (global and local) Iwasawa modules over (not necessarily commutative) Iwasawa algebras (mainly of $p$-adic Lie groups) over $\Z_p$ are established, which are very useful for determining certain properties of such modules in arithmetic applications. Slight generalizations of said results can be found in \citenospec{MR2333680} (for abelian groups and more general coefficient rings), \citenospec{MR1924402} (for products of not necessarily abelian groups, but with $\Z_p$-coefficients), and \citenospec{MR3084561}. Unfortunately, some of Jannsen's spectral sequences for families of representations as coefficients for (local) Iwasawa cohomology are still missing. We explain and follow the philosophy that all these spectral sequences are consequences or analogues of local cohomology and duality à la Grothendieck (and Tate for duality groups).

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