Global Fields

July 2 - 6, 2007, Moscow, Russia

Laboratoire J.-V. Poncelet

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Denis Osipov

Steklov Mathematical Institute, Russia

Gerbes and symbols

We consider construction of the 2-dimensional tame symbol on a 2-dimensional local field as monodromy of some combinatorial gerbe. From this construction we prove up to sign the Parshin reciprocity laws for these symbols for any algebraic surfaces over any perfect ground field.