On a generalization of Tate dualities with application to Iwasawa theory
On a Theorem of M. Deuring and I.R. Safarevic.
On algebraic tori of norm type.
On Artin-Verdier Duality for Function Fields.
On Demuskin groups with involution
On Galois groups of p-closed algebraic number fields with restricted ramification II.
On Galois groups of p-closed algebraic number fields with restricted ramification.
On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.
We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois...
On knots in algebraic number theory.
On -Ranks in the Class Field Tower Problem
Much recent progress in the 2-class field tower problem revolves around demonstrating infinite such towers for fields – in particular, quadratic fields – whose class groups have large 4-ranks. Generalizing to all primes, we use Golod-Safarevic-type inequalities to analyse the source of the -rank of the class group as a quantity of relevance in the -class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class groups...
On Solvable Number Fields.
On the Classification of Hermitian Forms.
On the cohomology of biquadratic extensions.
On the finiteness of for motives associated to modular forms.
On the Hasse norm principle.
On the ideal class groups of the maximal real subfields of number fields with all roots of unity
In this paper, for a totally real number field we show the ideal class group of is trivial. We also study the -component of the ideal class group of the cyclotomic -extension.
On the -torsion subgroup of the Brauer group of a number field
Given a number field Galois over the rational field , and a positive integer prime to the class number of , there exists an abelian extension (of exponent ) such that the -torsion subgroup of the Brauer group of is equal to the relative Brauer group of .
On the Shafarevich and Tate conjectures for hyperkähler varieties.
On the structure of certain Galois cohomology groups.