Finiteness of Frobenius Traces of a Sheaf on a Flat Arithmetic Scheme
2018 ◽
Vol 2020
(9)
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pp. 2864-2880
Keyword(s):
De Rham
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Abstract For a lisse $\ell $-adic sheaf on a scheme flat and of finite type over $\mathbb{Z}$, we consider the field generated over $ \mathbb{Q}$ by Frobenius traces of the sheaf at closed points. Assuming conjectural properties of geometric Galois representations of number fields and the Generalized Riemann Hypothesis, we prove that the field is finite over $\mathbb{Q}$ when the sheaf is de Rham at $\ell $ pointwise. This is a number field analog of Deligne’s finiteness result about Frobenius traces in the function field case.
2013 ◽
Vol 13
(3)
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pp. 517-559
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Keyword(s):
2017 ◽
Vol 164
(3)
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pp. 551-572
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Keyword(s):
2014 ◽
Vol 17
(A)
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pp. 385-403
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Keyword(s):
2013 ◽
Vol 149
(4)
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pp. 568-586
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Keyword(s):
Keyword(s):
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2007 ◽
Vol 03
(04)
◽
pp. 541-556
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2016 ◽
Vol 0
(0)
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