Geodesic
Compatibility of special value conjectures with the functional equation of zeta functions
Documenta mathematica, Tome 26 (2021), pp. 1633-1677.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove that the special value conjecture for the Zeta function $\zeta(\mathcal{X},s)$ of a proper, regular arithmetic scheme $\mathcal{X}$ that we formulated in [\textit{M. Flach} and \textit{B. Morin}, Doc. Math. 23, 1425--1560 (2018; Zbl 1404.14024)] is compatible with the functional equation of $\zeta(\mathcal{X},s)$ provided that the rational factor $C(\mathcal{X},n)$ we were not able to compute previously has the simple explicit form given in the introduction below.
Classification : 11G40, 14F40, 14F25
Keywords: arithmetic schemes, zeta-values, functional equation, Weil-étale cohomology 
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     author = {Flach, Matthias and Morin, Baptiste},
     title = {Compatibility of special value conjectures with the functional equation of zeta functions},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a12/}
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Flach, Matthias; Morin, Baptiste. Compatibility of special value conjectures with the functional equation of zeta functions. Documenta mathematica, Tome 26 (2021), pp. 1633-1677. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a12/