shuji_saito

八ヶ岳ワークショップ, 2017

Topological Hochschild homology and integral p-adic Hodge theory

日時: 2017年9月21日(木)-24日(日)

場所: 八ヶ岳自然文化園: 長野県諏訪郡原村17217-1613

過去の研究集会:

2014年 | 2016年 |

研究集会組織委員(Organizers):

Lars Hesselholt(Copenhagen), 佐藤周友(中央大), 宮崎弘安(東京大学),岩佐亮明(東京大学),斎藤秀司 (東工大)

Speakers

Federico Binda, Lars Hesselholt,Akhil Mathew, Kei Hagihara, Teruhisa Koshikawa, Jun Yoshida, Martin Speirs, Mariko Ohara, Wataru Kai,Hiroyasu Miyazaki,Ryoumei Iwasa

この研究集会は以下の援助のもとに開催されます

日本学術振興会科学研究費(基盤B) #17H02832 代表者 加藤文元.

Program

21(Thur)/Sep:

9:00-10:00 Hesselholt, "The big picture": THH, TP, weight filtration, p-adic Hodge theory

10:30-12:30 Hagihara, "Topological Hochschild homology": Some background on higher algebra and E_{\infty}-rings. Topological Hochschild homology for E_{\infty}-algebras.

14:00-15:30 Iwasa, "The cyclotomic structure of THH": The Tate construction, the Tate diagonal, and the Frobenius on THH.

16:00-17:30 Binda, "Topological cyclic homology": TC^{-}, TP, and TC. Tate orbit lemma and TR^n.

22(Fri)/Sep:

9:00-10:30 Kai and Miyazaki, "DRW and TR": Definition of DRW and the map DRW --> TR.

11:00-12:30 Kay and Miyazaki, "Smooth algebras": Behavior of THH and TR under etale and polynomial extensions.

14:00-15:30 Yoshida, "\pi_*(\mathbb{F}_p \otimes \mathbb{F}_p) after Milnor": The Hopf algebroid structure of \pi_*(R \otimes_A R); Milnor's calculation for R = \mathbb{F}_p and A = S; the action of the Araki-Kudo-Dyer-Lashof operations thereom.

16:00-17:30 Speirs, "Bokstedt periodicity": Bokstedt's calculation of THH_*(F_p).

23(Sat)/Sep:

9:00-10:30 Ohara, "THH of schemes": Descent and hypercohomology spectra. Mirror duality.

11:30-12:30 Iwasa, "fppf descent": Bhatt's theorem on fppf descent for the cotangent complex, HH, and THH.

15:30-17:30 Mathew, "Weight filtration on THH": Construction of the weight filtration on THH (and if possible TP).

24(Sun)/Sep:

9:00-10:30 Mathew, "Identification of the graded pieces": Calculation of THH for R/F_p regular semiperfect and identification of the graded pieces of the weight filtration.

11:00-12:30 Koshikawa, "q-DR": The BMS complex A\OMega and the q-DR complex.

16:00-17:30 Hesselholt, "Zeta functions": Deninger's picture and TP.

18:00-20:30 Discussions.