Семинары: И. Амрани,

СЕМИНАРЫ


Петербургский топологический семинар им. В. А. Рохлина 9 марта 2015 г. 17:30, г. Санкт-Петербург, ПОМИ, комн. 311 (наб. р. Фонтанки, 27)

[Analogy between the cyclotomic trace map $K\to TC$ and the Grothendieck trace formula via noncommutative geometry] I. Amrani Санкт-Петербургский академический университет — научно-образовательный центр нанотехнологий РАН (Академический университет)
Аннотация: There will be a little algebraic geometry, number theory and algebraic K-theory. We suggest a categorification procedure in order to capture an analogy between Crystalline Grothendieck–Lefschetz trace formula and the cyclotomic trace map $K\to TC$ from the algebraic K-theory to the topological cyclic homology $TC$. First, we categorify the category of schemes to the $(2,\infty)$-category of noncommuatative schemes a la Kontsevich. This gives a categorification of the set of rational points of a scheme. Then, we categorify the Crystalline Grothendieck–Lefschetz trace formula and find an analogue to the Crystalline cohomology in the setting of noncommutative schemes over $\mathbb F_p$. Our analogy suggests the existence of a categorification of the $l$-adic cohomology trace formula in the noncommutative setting for $l$ different from $p$. Finally, we write down the corresponding dictionary. Язык доклада: английский