JournalsjemsVol. 24, No. 3pp. 967–1005

Exterior powers in Iwasawa theory

  • Frauke M. Bleher

    University of Iowa, Iowa City, USA
  • Ted Chinburg

    University of Pennsylvania, Philadephia, USA
  • Ralph Greenberg

    University of Washington, Seattle, USA
  • Mahesh Kakde

    Indian Institute of Science, Bangalore, India
  • Romyar Sharifi

    University of California, Los Angeles, USA
  • Martin J. Taylor

    University of Oxford, UK
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The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-pp Galois groups with ramification allowed at a maximal set of primes over pp such that the module is torsion. A main conjecture for such an Iwasawa module describes its codimension one support in terms of a pp-adic LL-function attached to the primes of ramification. In this paper, we study more general and potentially much smaller modules that are quotients of exterior powers of Iwasawa modules with ramification at a set of primes over pp by sums of exterior powers of inertia subgroups. We show that the higher codimension support of such quotients can be measured by finite collections of characteristic ideals of classical Iwasawa modules, hence by pp-adic LL-functions under the relevant CM main conjectures.

Cite this article

Frauke M. Bleher, Ted Chinburg, Ralph Greenberg, Mahesh Kakde, Romyar Sharifi, Martin J. Taylor, Exterior powers in Iwasawa theory. J. Eur. Math. Soc. 24 (2022), no. 3, pp. 967–1005

DOI 10.4171/JEMS/1115