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For an abelian variety $A$ over a local number field, the Tamagawa number of $A$ is the number of connected components of its Néron model.

For a smooth projective curve $X/\Q$ the Tamagawa number of $X$ at at a prime $p$ is the Tamagawa number of the base change of its Jacobian to the field $\Q_p$.

It is a positive integer that is equal to 1 at all primes of good reduction for the Jacobian; it may also be 1 at primes of bad reduction.

The product of the Tamagawa numbers over all primes is a positive integer known as the Tamagawa product.

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• Last edited by Andrew Sutherland on 2020-01-03 22:19:49
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