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>
 
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