TECHNION FACULTY OF MATHEMATICS ALGEBRA SEMINAR SPEAKER: Rony Bitan, Technion. TOPIC: The discriminant of an algebraic torus. DATE: Thursday, Jan. 13, 2011 TIME: 12:30 PLACE: Amado 719 Abstract: Let T be an algebraic torus defined over a local field K with discrete valuation ring O and finite residue field k. As T(K) is locally compact, it admits a multiplicative Haar measure which is unique up to a scalar multiplication. Let T(O) be the maximal compact subgroup of T(K). Its volume with respect to such a normalized measure is an arithmetic invariant which plays an important role in the quasi-discriminant formulated by Ono and Shyr for tori defined over global fields. We use the standard integral model defined by Voskresenskii and its reduction over k in order to describe the structure of T(O) and measure it. Due to a construction of Kottwitz, the result is expressed in terms of the cocharacter group of T. <http://www.technion.ac.il/~neftind/algebra_seminar.htm> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Jack Sonn <sonn@math.technion.ac.il>