for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the étale fundamental group. COUNT 4
QSN1 What concepts are fundamental to number theory? ANS1 adele rings and adelic algebraic groups QSN2 What group uses infinite field extensions with topology? ANS2 the absolute Galois group QSN3 What is used to generalize the connection of fields and groups to infinite field extensions? ANS3 Krull topology QSN4 What group is an advanced observation of infinite field extensions and groups that is adapted for the needs of algebraic geometry? ANS4 the étale fundamental group