High Quality Content by WIKIPEDIA articles! The conjectures for (a) are called Beilinson's conjectures, for Alexander Beilinson. The idea is to abstract from the regulator of a number field to some "higher regulator", a determinant constructed on a real vector space that comes from algebraic K-theory. The conjectures for (b) are called the Bloch–Kato conjectures for special values (for Spencer Bloch and Kazuya Kato – NB this circle of ideas is distinct from the Bloch–Kato conjecture of K-theory, extending the Milnor conjecture, a proof of which was announced in 2009). For the sake of greater clarity they are also called the Tamagawa number conjecture, a name arising via the Birch–Swinnerton–Dyer conjecture and its formulation as an elliptic curve analogue of the Tamagawa number problem for linear algebraic groups.

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