The Schur subgroup of a 2-adic field*

Uniform Distribution and the Schur Subgroup

In this paper we continue the investigation into the group of algebras with uniformly distributed invariants U(K), and its relation to the Schur subgroup, undertaken in [9]. The notation is the same as in [9]. In the first section we investigate the index 1 U(K), : S(K), 1 where q is an odd prime. We obtain [9, Theorem 2.71 as a special case of Theorem 1.2, wherein we obtain that the above inde...

Globally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change‎, ‎I‎ : ‎Iwasawa algebras and a base change map

This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎mathbb{Z}_p)$‎. ‎It then describes a natural base change map between the Iwasawa algebras or more correctly‎, ‎as it turns out‎, ‎between the global distribut...

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Chow group of 0-cycles on surface over a p-adic field with infinite torsion subgroup

We give an example of a projective smooth surface X over a p-adic field K such that for any prime l different from p, the l-primary torsion subgroup of CH0(X), the Chow group of 0-cycles on X, is infinite. A key step in the proof is disproving a variant of the Block-Kato conjecture which characterizes the image of an l-adic regulator map from a higher Chow group to a continuous étale cohomology...

The mod 2 homology of the general linear goup of a 2-adic local field

Let F be a finite extension of Q2, of degree d. Our first main theorem gives an explicit computation of the mod two homology Hopf algebra of the infinite general linear group GLF . The answer is formulated in terms of the well-known homology algebras of the infinite unitary group U, its classifying space BU, and the classifying space BO of the infinite orthogonal group. Let P denote the subalge...