Divisibility results for zero-cycles

Gazaki, Evangelia; Hiranouchi, Toshiro

doi:10.1007/s40879-021-00471-y

Cited by 3 publications

(2 citation statements)

References 41 publications

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“…It then follows by [Kaw02, Theorem 2.1.6], (see also [GH21,Prop. 3.13]) that the homomorphism δ induces an isomorphism (3.9)…”

Section: Explicit Isomorphismmentioning

confidence: 99%

“…LvLv . It follows by [Kaw02, Lemma 2.1.5] (see also[GH21, Lemma 3.5]) that the extension k 0 /L v is totally ramified of degree p with the jump in the ramification filtration of Gal(k 0 /L v ) happening at s = p − 1. It then follows by [Ser79, V.3, Corollary 7] that there exists a unit u ∈ U p−1 Lv such that the symbol algebra (δ(A v ), u) p is nontrivial in Br(L v ) p .…”

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confidence: 99%

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Weak Approximation for $0$-cycles on a product of elliptic curves

Gazaki¹,

Koutsianas²

2021

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In the 1980's Colliot-Thélène, Sansuc, Kato and S. Saito proposed conjectures related to local-to-global principles for 0-cycles on arbitrary smooth projective varieties over a number field. We give some evidence for these conjectures for a product X = E 1 × E 2 of two elliptic curves. In the special case when X = E ×E is the self-product of an elliptic curve E over Q with potential complex multiplication, we show that the places of good ordinary reduction are often involved in a Brauer-Manin obstruction for 0-cycles over a finite base change. We give many examples when these 0-cycles can be lifted to global ones.

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“…It then follows by [Kaw02, Theorem 2.1.6], (see also [GH21,Prop. 3.13]) that the homomorphism δ induces an isomorphism (3.9)…”

Section: Explicit Isomorphismmentioning

confidence: 99%

mentioning

confidence: 99%