Geodesic
On the minus component of the equivariant Tamagawa number conjecture for $\mathbb{G}_m$
Documenta mathematica, Tome 28 (2023) no. 2, pp. 419-511
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The equivariant Tamagawa number conjecture (hereinafter called the eTNC) predicts close relationships between algebraic and analytic aspects of motives. In this paper, we prove a lot of new cases of the minus component of the eTNC for Gm​ and for CM abelian extensions. One of the main results states that the p-component of the eTNC is true when there exists at least one p-adic prime that is tamely ramified. The fundamental strategy is inspired by the work of Dasgupta and Kakde on the Brumer–Stark conjecture.
DOI : 10.4171/dm/914
Classification : 11R42, 11R29
Mots-clés : Class groups, L-functions, equivariant Tamagawa number conjecture 
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     author = {Mahiro Atsuta and Takenori Kataoka},
     title = {On the minus component of the equivariant {Tamagawa} number conjecture for $\mathbb{G}_m$},
     journal = {Documenta mathematica},
     pages = {419--511},
     year = {2023},
     volume = {28},
     number = {2},
     doi = {10.4171/dm/914},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/914/}
}
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Mahiro Atsuta; Takenori Kataoka. On the minus component of the equivariant Tamagawa number conjecture for $\mathbb{G}_m$. Documenta mathematica, Tome 28 (2023) no. 2, pp. 419-511. doi: 10.4171/dm/914

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