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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…mehr

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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.