Ramification groups of a local field (with Ahmed Abbes and Kazuya Kato)

Takeshi Saito
2019-09-05 10:00—11:30
N202


时间:2019年9月4日(周三)9:45—10:45
地点:南楼202
报告人:Takeshi Saito (斋藤毅 东京大学)
题目:Characteristic cycle of an l-adic sheaf
摘要:
For an l-adic sheaf on a smooth variety over a perfect field of characteristic p >= 0, its characteristic cycle is defined as a cycle supported on the singular support, defined by Beilinson as a conical closed subset of the cotangent bundle of the variety. This is an algebraic analogue of that constructed by Kashiwara-Schapira in a transcendental setting.

时间:2019年9月5日(周四)10:00—11:30
地点:南楼202
报告人:Takeshi Saito (斋藤毅 东京大学)
题目:Ramification groups of a local field (with Ahmed Abbes and Kazuya Kato)
摘要:
For a Galois extension of a discrete valuation field with not necessarily perfect residue field, two filtrations (logarithmic and non-logarithmic) by ramification groups are defined by a geometric method by Abbes and myself. For an abelian extension, another filtration is defined earlier by Kato by a cohomological method. After briefly recalling the definition, we discuss a recent result with Kato on the equality of Kato's filtration with the logarithmic filtration.