Reciprocity Laws for the Higher Tame Symbol and the Witt Symbol on an\n Algebraic Surface

2013/04/23 by Kirsty Syder, Syder, Kirsty
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.1304.6250

Abstract

Parshin's higher Witt pairing on an arithmetic surface can be combined with\nthe higher tame pairing to form a symbol taking values in the absolute abelian\nGalois group of the function field. We prove reciprocity laws for this symbol\nusing techniques of Morrow for the Witt symbol and Romo for the higher tame\nsymbol.\n

Citations

• On the structure and ideal theory of complete local rings

Related

• A refinement of the Parshin symbol for surfaces
• Ramification theory of reciprocity sheaves, II, Higher local symbols
• To the multidimensional tame symbol
• Reciprocity law for compatible systems of abelian mod p Galois representations
• Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an artinian local ring