A generalization of the Contou-Carrère symbol

A new explicit expression of the Contou-Carrère symbol

“…The author has also obtained a similar result for an algebraic curve over a perfect field [10], and A. Beilinson, S. Bloch and H. Esnault [3] have defined the ContouCarrère symbol as the commutator pairing in a Heisenberg super extension. Moreover, recently, this symbol has played an important role in the work of M. Kapranov and E. Vasserot [6], and M. Asakura [2] has shown that the Contou-Carrère symbol coincides with the boundary map δ : K i+1 (A((t))) −→ K i (A) described by K. Kato in [7].…”

A direct proof of the Steinberg property of the Contou-Carrère symbol

“…Moreover, the author has obtained a similar result for an algebraic curve over a perfect field [10], and A. Beilinson, S. Bloch and H. Esnault [3] have defined the Contou-Carrère symbol as the commutator pairing in a Heisenberg super extension. This symbol has also played an important role in a recent work by M. Kapranov and E. Vasserot [6].…”

An Algebraic-Geometric Method for Constructing Generalized Local Symbols on Curves

“…Moreover, recently, Beilinson et al [3] have defined the ContouCarrère symbol as the commutator pairing in a Heisenberg super extension. This article gives the relation between the classic datum used to define a local symbol (a closed point of a curve) and the formal scheme that appears in [15]. As far as we know, generalized local symbols, different from the symbols referred to previously, have not been stated explicitly in the literature.…”

“…We should remark that generalizations of the tame symbol have been made by Contou-Carrère [5] as a morphism of functors and by the author as a morphism of schemes [15]. Moreover, recently, Beilinson et al [3] have defined the ContouCarrère symbol as the commutator pairing in a Heisenberg super extension.…”