Codimension 2
From Mathematics
(→Introduction) |
(→Introduction) |
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In the end of the 70's a beautiful story began, when mathematicians, with Bloch leading the way, began to discover a | In the end of the 70's a beautiful story began, when mathematicians, with Bloch leading the way, began to discover a | ||
beautiful connection between algebraic K-Theory, algebraic cycles and polylogarithms. The first work was restricted to the | beautiful connection between algebraic K-Theory, algebraic cycles and polylogarithms. The first work was restricted to the | ||
− | case of codimension 2 cycles, K_2, and the | + | case of codimension 2 cycles, K_2, and the dilogarithm (this next polylogarithm after the usual logarithm) and quite explicit. |
This story later triggered an enormous amount of research and was the motivation for many modern developments and conjectures, as for example | This story later triggered an enormous amount of research and was the motivation for many modern developments and conjectures, as for example | ||
the theory of higher algebraic K-Theory (Quillen), mixed motives (Voevodsky - the ideas going back to Grothendieck), motivic cohomology, Bloch-Kato conjecture, ... | the theory of higher algebraic K-Theory (Quillen), mixed motives (Voevodsky - the ideas going back to Grothendieck), motivic cohomology, Bloch-Kato conjecture, ... |