Timeline for Monsky's proof of the finiteness of de Rham cohomology
Current License: CC BY-SA 3.0
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| Sep 3, 2012 at 0:35 | comment | added | Filippo Alberto Edoardo | The "shifting argument" simply means that if you have a complex $C_\dot$, then the complex $\cdots\to C_0\stackrel{0}{\to}C_0$ has the same homology. And this is what happens in Monsky's paper, by observing $A_f/A=A[T]/(\partial_T+L_f)A[T]$. Tha arrows are simply $x\wedge(e_1\wedge\dots\wedge e_s)\mapsto \bar{x}\wedge(e_1\wedge\dots\wedge e_s)$ where "bar" is reduction $\pmod{(\partial_T+L_f)A[T]}$. | |
| Sep 1, 2012 at 13:04 | comment | added | Lierre | Thanks ! So know I understand the lemma, and I can write a proof of it with the explicit map of complexes from the second (in the lemma) to the first, given by $\alpha + \beta\wedge e_{n+1} \mapsto \alpha$, and checking everything. However, I hardly understand why you and Monsky can curcumvent this computation. Is that just trivial for someone used to Koszul homology ? I'm not sure to understand you shifting argument. | |
| Sep 1, 2012 at 6:58 | history | answered | Filippo Alberto Edoardo | CC BY-SA 3.0 |