ON THE SECOND COHOMOLOGY OF THE NORM ONE GROUP OF A p-ADIC DIVISION ALGEBRA
نویسنده
چکیده
Let F be a p-adic field, that is, a finite extension of Qp. Let D be a finite dimensional division algebra over F and let SL1(D) be the group of elements of reduced norm 1 in D. Prasad and Raghunathan proved that H(SL1(D),R/Z) is a cyclic p-group whose order is bounded from below by the number of p-power roots of unity in F , unless D is a quaternion algebra over Q2. In this paper we give an explicit upper bound for the order of H(SL1(D),R/Z) for p ≥ 5, and determine H(SL1(D),R/Z) precisely when F is cyclotomic, p ≥ 19 and the degree of D is not a power of p.
منابع مشابه
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.
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