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Summer 1999 An injectivity result for Hermitian forms over local orders
Laura Fainsilber, Jorge Morales
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Illinois J. Math. 43(2): 391-402 (Summer 1999). DOI: 10.1215/ijm/1255985221


Let $\Lambda$ be a ring endowed with an involution $a \mapsto \tilde{a}$. We say that two units $a$ and $b$ of $\Lambda$ fixed under the involution are congruent if there exists an element $u \in \Lambda^{\times}$ such that $a = ub\tilde{u}$. We denote by $\mathcal{H}(\Lambda)$ the set of congruence classes. In this paper we consider the case where $\Lambda$ is an order with involution in a semisimple algebra $A$ over a local field and study the question of whether the natural map $\mathcal{H}(\Lambda) \rightarrow \mathcal{H}(\Lambda)$ induced by inclusion is injective. We give sufficient conditions on the order $\Lambda$ for this map to be injective and give applications to hermitian forms over group rings.


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Laura Fainsilber. Jorge Morales. "An injectivity result for Hermitian forms over local orders." Illinois J. Math. 43 (2) 391 - 402, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0939.11020
MathSciNet: MR1703194
Digital Object Identifier: 10.1215/ijm/1255985221

Primary: 11E39
Secondary: 11E08 , 11E70 , 19G38

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 2 • Summer 1999
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