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https://en.wikipedia.org/wiki/Cohomology_with_compact_support
called the long exact sequence of cohomology with compact support. It has numerous applications, such as the Jordan curve theorem, which is obtained for X = R² and Z a simple closed curve in X. De Rham cohomology with compact support satisfies a covariant Mayer–Vietoris sequence: if U and V are open sets covering X, then
https://arxiv.org/abs/1002.0105v1
Abstract: We discuss Parshin's conjecture on rational K-theory over finite fields and its implications for motivic cohomology with compact support.Author: T. Geisser
http://claymath.org/library/monographs/cmim02.pdf
Lecture notes on motivic cohomology / Carlo Mazza, Vladimir Voevodsky, Charles A. Weibel. ... Etale motivic cohomology and algebraic singular homology 75´ ... Motives with compact support 128 Part 5. Higher Chow Groups 133 Lecture 17. Higher Chow groups 135 Appendix 17A. Cycle maps 143
https://arxiv.org/pdf/math/0405164.pdf
mology and etale cohomology proved in [6] carry over to the present situation. The groups Hi c (X ar,Z(n)) are defined as the Weil-eh cohomology groups with compact support of the motivic complex Z(n) of Suslin-Voevodsky (we set Z(n) = colimpm µ⊗mn[−1] for n < 0). Arithmetic cohomology groups are ex-pected to satisfy the following
https://www.amazon.com/Transfers-Motivic-Homology-Theories-Mathematics/dp/0691048150
Sep 01, 2002 · The authors detail to what extent the higher Chow groups can be considered to be a motivic cohomology theory. Motivic homology, motivic cohomology, and Borel-Moore motivic cohomology are shown to be related to the bivariant cycle cohomology and their algebraic topological properties discussed briefly.Cited by: 273
https://thesis.library.caltech.edu/11598/8/LawlessHughesNathaniel2019.pdf
ality of cohomology groups ( [Ber97b]), and in the case of smooth schemes a Poncairé duality and Künneth formula ( [Ber97a]). On the other hand, we can consider construction on the motivic side: motivic cohomology, motivic cohomology with compact support, Borel-Moore motivic homology, and motivic homology. We can also consider the étale ...
https://math.stackexchange.com/questions/770201/show-that-the-compactly-supported-de-rham-cohomology-groups-hp-dr-mathbb
$\begingroup$ The way Lee proves poincare duality uses this fact about compactly supported De Rham cohomology, so I wonder if there is a way to tackle this problem directly? $\endgroup$ – …
https://www.researchgate.net/publication/45898444_Parshin's_conjecture_and_motivic_cohomology_with_compact_support
We discuss Parshin's conjecture on rational K-theory over finite fields and its implications for motivic cohomology with compact support. Do you want to read the rest of this article? Request full ...
http://pcwww.liv.ac.uk/~guletski/papers/Anwar%20Thesis%20June%202017.pdf
a motivic measure, as it does not respect the scissors relations. Then, one may consider altering motivic spaces to induce a functor that gives rise to a motivic measure. Some motivic measures, like the Hodge measure and the ‘-adic measure arise from cohomology theories with proper1 support, i.e. they satisfy the excision property,(E).
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