清华主页 EN
导航菜单

Motivic Cohomology

来源: 03-16

时间:08:50 - 10:35, every Wednesday,Friday, 3/16/2022 - 6/8/2022

地点:1110&Zoom ID:638 227 8222,密码:BIMSA

组织者:杨南君

主讲人:杨南君

 要:

Motivic cohomology, originated from Deligne, Beilinson and Lichtenbaum and developed by Voevodsky, is a kind of cohomology theory on schemes. It admits comparison with étale cohomology of powers of roots of unity (Beilinson-Lichtenbaum), together with higher Chow groups, and relates to K-theory by Atiyah-Hirzebruch spectral sequence. In this lecture, we establish the category of motives in which the motivic cohomologies are realized. We explain its relationship with Milnor K-theory and Chow group. Furthermore, we introduce devices like MV-sequence, Gysin triangle, projective bundle formula and duality.


预备知识:

Basic algebraic geometry (GTM 52, Chapter 1-3)


参考书目:

C. Mazza, V. Voevodsky, C. Weibel, Lecture Notes on Motivic Cohomology, American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA (2006).


主讲人简介:

本人本科毕业于北京航空航天大学,硕士博士毕业于格勒诺布尔-阿尔卑斯大学,博士导师Jean Fasel。之后在丘成桐数学科学中心做博后,现在是BIMSA的助理研究员。本人研究方向为原相(motivic)上同调和周-威特(Chow-Witt)环。本人提出了分裂型米尔诺-威特原相理论并且应用在纤维丛的周-威特环的计算中。相关成果已经独立发表在Manus. Math.Doc. Math.等期刊上。


Note link:

【1】 【2】 【3】 【4】 【5】 【6】 【7】 【8】 【9】 【10】 【11】 【12】 【13】 【14】 【15】 【16】【17】 【18】 【19】 【20】 【21】 【22】 【23】

Video link:

【1】(Passcode: 508!pfJL)

【2】(Passcode: W.p?p3@j)

【3】(Passcode: O0A#NuE$)

【4】(Passcode: A0Js.uaU)

【5】(Passcode: X9kFtwx@)

【6】(Passcode: 0Feiyif%)

【7】(Passcode: L02GL=1?)

【8】(Passcode: Y#B0^Sf4)

【9】(Passcode: 6sYf!kFe)

【10】(Passcode: 0Fi#5*@L)

【11】(Passcode: 6V!Nz75c)

【12】(Passcode: @7!*J?Ut)

【13】(Passcode: F#^%6@%6)

【14】(Passcode: r0Yi2gw$)

【15】(Passcode: QnrL47*a)

【16】(Passcode: ^1ZRdrgf)

【17】(Passcode: EMLFm17+)

【18】(Passcode: @j0m*.9k)

【19】(Passcode: aDQ@5p!w)

【20】(Passcode: 44@.7EbH)

【21】(Passcode: 2&b33u7u)

【22】(Passcode: %8L5DhtY)


返回顶部
相关文章
  • Introduction to Prismatic cohomology

    Record: NoLevel: GraduateLanguage: EnglishPrerequisiteAlgebraic geometry (background in algebraic number theory will be helpful)AbstractPrismatic cohomology, which is developed in a recent work of Bhatt-Scholze, is a cohomology theory for schemes over p-adic rings. It is considered to be an overarching cohomology theory in p-adic geometry, unifying etale, de Rham, and crystalline cohomology. Du...

  • Quadratic conductor formulas for motivic spectra

    AbstractWe use the machinery of A1-homotopy theory to study the geometric ramification theory. We define the quadratic Artin conductor for a motivic spectrum on a smooth proper curve and obtain a quadratic refinement of the classical Grothendieck-Ogg-Shafarevich formula. Then we use the non-acyclicity class to formulate a quadratic conductor formula. In some sense, we obtain a quadratic version...