Tate modules of isocrystals and good reduction of Drinfeld modules
نویسندگان
چکیده
A Drinfeld module has a $\mathfrak{p}$-adic Tate not only for every finite place $\mathfrak{p}$ of the coefficient ring but also $\mathfrak{p} = \infty$. This was discovered by J.-K. Yu in form representation Weil group. Following an insight Taelman we construct $\infty$-adic means theory isocrystals. applies more generally to pure $A$-motives and $F$-isocrystals $p$-adic cohomology theory. We demonstrate that good reduction if its is unramified. The key proof Hartl Pink which gives analytic classification vector bundles on Fargues-Fontaine curve equal characteristic.
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15 صفحه اولThe Sato-tate Law for Drinfeld Modules
We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module φ defined over a field L, he constructs a continuous representation ρ∞ : WL → D× of the Weil group of L into a certain division algebra, which encodes the Sato-...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2021
ISSN: ['1944-7833', '1937-0652']
DOI: https://doi.org/10.2140/ant.2021.15.909