$SK_1$ of $p$-adic group rings

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...

Group Rings over the p-Adic Integers

A NOTE ON p-ADIC INVARIANT INTEGRAL IN THE RINGS OF p-ADIC INTEGERS

In [2], I constructed the p-adic q-integral I q (f) on Z p. In this paper, we consider the properties of lim q→−1 I q (f) = I −1 (f). Finally we give the some applications of I −1 (f) and integral equations for I −1 (f). These properties are useful and worthwhile to study Euler numbers and polynomials.

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

WITT VECTORS WITH p-ADIC COEFFICIENTS AND FONTAINE’S RINGS

We describe an alternate construction of some of the basic rings introduced by Fontaine in p-adic Hodge theory. In our construction, the central role is played by the ring of p-typical Witt vectors over a p-adic valuation ring, rather than theWitt vectors over a ring of positive characteristic. This suggests the possibility of forming a meaningful global analogue of p-adic Hodge theory.