Hasse principle [SEP] named after
Hasse principle
In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the "p"-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have
Manin obstruction
In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety "X" over a global field, which measures the failure of the Hasse principle for "X". If the value of the obstruction is non-trivial, then "X" may have points over all local fields but not over the global field. The Manin obstruction is sometimes called the Brauer–Manin obstruction, as Manin used the Brauer group of X to define