The Motivic Group H−1,−1BM
2019 ◽
pp. 95-102
This chapter develops some more of the properties of the Borel–Moore homology groups 𝐻𝐵𝑀 −1,−1(𝑋). It shows that it is contravariant in 𝑋 for finite flat maps, and has a functorial pushforward for proper maps. If 𝑋 is smooth and proper (in characteristic 0), 𝐻𝐵𝑀 −1,−1(𝑋) agrees with 𝐻2𝒅+1,𝒅+1(𝑋, ℤ), and has a nice presentation, which this chapter explores in more depth. The main result in this chapter is the proposition that: if 𝑋 is a norm variety for ª and 𝑘 is 𝓁-special then the image of 𝐻𝐵𝑀 −1,−1(𝑋) → 𝑘× is the group of units 𝑏 such that ª ∪ 𝑏 vanishes in 𝐾𝑀 𝑛+1(𝑘)/𝓁. Again, this chapter also explores the historic trajectory of its equations.
1992 ◽
Vol 45
(3)
◽
pp. 503-506
◽
Keyword(s):
1986 ◽
Vol 1986
(371)
◽
pp. 216-220
Keyword(s):
1993 ◽
Vol 68
(1)
◽
pp. 653-672
◽
Keyword(s):
2010 ◽
Vol 362
(10)
◽
pp. 5501-5501
◽
Keyword(s):
2008 ◽
Vol 17
(10)
◽
pp. 1199-1221
◽