Timeline for Equivalent definitions of the Hasse invariant
Current License: CC BY-SA 3.0
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| Apr 15, 2016 at 1:23 | comment | added | nfdc23 | The formal completion of the Tate curve along 0 is (via Raynaud's construction, upon which the proofs of the black-boxed properties in K-M all depend) is the formal completion of $\mathbf{G}_m$ along its identity section in such a way that (by comparison on cotangent spaces along identity section) the 1-form "$dq/q$" on the Tate curve goes over to $dt/t$ on $\mu_p$, whose tangent space over an $\mathbf{F}_p$-algebra agrees with that of $\mathbf{G}_m$. To deduce $A$ has $q$-expansion 1, by functoriality and base change compatibility of $V_{G/S}$ we use that $V_{\mu_p/\mathbf{F}_p}={\rm{id}}$. | |
| Apr 14, 2016 at 23:49 | history | asked | Bear | CC BY-SA 3.0 |