Journal of the Ramanujan Mathematical Society

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Tamagawa Torsors of an Abelian Variety


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1 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ-85287, United States
     

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For an abelian variety A/K over a number field K, we define the set of Tamagawa torsors of A at a prime υ of K to be the set of principal homogeneous spaces of A over the completion Kυ of K at υ that are split by an unramified extension of Kυ. In this paper, we study some of the arithmetic properties of the Tamagawa torsors.We also give, following Mazur’s theory of visibility, conditions under which non-trivial elements of the Tamagawa torsors of A may be interpreted as rational points on another abelian variety B.
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  • Tamagawa Torsors of an Abelian Variety

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Authors

Saikat Biswas
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ-85287, United States

Abstract


For an abelian variety A/K over a number field K, we define the set of Tamagawa torsors of A at a prime υ of K to be the set of principal homogeneous spaces of A over the completion Kυ of K at υ that are split by an unramified extension of Kυ. In this paper, we study some of the arithmetic properties of the Tamagawa torsors.We also give, following Mazur’s theory of visibility, conditions under which non-trivial elements of the Tamagawa torsors of A may be interpreted as rational points on another abelian variety B.