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Linkage of sets of cyclic algebras

Authors:	Adam Chapman

Institution:	1. Universidad de Cádiz, Puerto Real, Cádiz, Spain;2. CMCC, Universidade Federal do ABC, Santo André, Brazil;3. CMUP, Faculdade de Ciências, Universidade do Porto, Porto, Portugal;4. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia;5. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil;6. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal;7. Saint Petersburg University, Saint Petersburg, Russia;1. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India;2. Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502285, Telangana, India;1. Utah State University, Department of Mathematics and Statistics, Logan UT 84341, USA;2. Hung Vuong University, Faculty of Natural Sciences, Viet Tri, Phu Tho, Viet Nam;3. Université Bretagne Sud, Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, Campus de Tohannic, BP 573 F-56017 Vannes, France

Abstract:	Let p be a prime integer and F the function field in two algebraically independent variables over a smaller field $F_{0}$ . We prove that if $char (F_{0}) = p ? 3$ then there exist $p^{2} ? 1$ cyclic algebras of degree p over F that have no maximal subfield in common, and if $char (F_{0}) = 0$ then there exist $p^{2}$ cyclic algebras of degree p over F that have no maximal subfield in common.

Keywords:	Division algebras Cyclic algebras Valuation theory Linkage Fields of positive characteristic
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