中科院数学与系统科学研究院

数学研究所

 

数论研讨班

 

报告人 Shuji SaitoUniversity of Tokyo

 A motivic construction of ramification filtrations

  2018.11.14(星期三),17:00-18:00

  点:数学院南楼N913室(视频)

  : We give a new interpretation of Artin conductors of characters in the framework of theory of motives with modulus. It gives a unified way to understand Artin conductors of characters and irregularities of line bundle with integrable connections as well as overconvergent F-isocrystals of rank 1. It also gives rise to new conductors, for example, for G-torsors with G a finite flat group scheme, which specializes to the classical Artin conductor in case G = Z/nZ. We also give a motivic proof of a theorem of Kato and Matsuda on the determination of Artin conductors along divisors on smooth schemes by its restrictions to curves. Its proof is based on a motivic version of a theorem of Gabber-Katz. This is a joint work with Kay Rulling.

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