A categorical proof of the Parshin reciprocity laws on algebraic surfaces

作者：Osipov Denis^*; Zhu Xinwen

来源：Algebra and Number Theory, 2011, 5(3): 289-337.

• Picard groupoids
• central extensions
• commutator maps
• two-dimensional local fields
• higher adeles
• reciprocity laws

We define and study the 2-category of torsors over a Picard groupoid, a central extension of a group by a Picard groupoid, and commutator maps in this central extension. Using this in the context of two-dimensional local fields and two-dimensional adele theory we obtain the two-dimensional tame symbol and a new proof of Parshin reciprocity laws on an algebraic surface.

• 出版日期2011