On the axiomatisation of C_p with roots of unity.
By Romain Rioux
In the middle of the 90’s Tate and Voloch have proved a result concerning the sums of roots of unity with fixed coefficients. By using an adapted decomposition to understand the p-adic valuation of these sums we will see how to improve their result and using it to axiomatize the valued structure Cp with a predicate for the group of roots of unity.