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Abstract Let $$E$$ be an elliptic curve defined over $${\mathbb{Q}}$$ of conductor $$N$$, $$p$$ an odd prime of good ordinary reduction such that $E[p]$ is an irreducible Galois module, and $$K$$ an imaginary quadratic field with all primes dividing $Np$ split. We prove Iwasawa main conjectures for the $${\mathbb{Z}}_{p}$$-cyclotomic and $${\mathbb{Z}}_{p}$$-anticyclotomic deformations of $$E$$ over $${\mathbb{Q}}$$ and $K,$ respectively, dispensing with any of the ramification hypotheses on $E[p]$ in previous works. The strategy employs base change and the two-variable zeta element associated to $$E$$ over $$K$$, via which the sought after main conjectures are deduced from Wan’s divisibility towards a three-variable main conjecture for $$E$$ over a quartic CM field containing $$K$$ and certain Euler system divisibilities. As an application, we prove cases of the two-variable main conjecture for $$E$$ over $$K$$. The aforementioned one-variable main conjectures imply the $$p$$-part of the conjectural Birch and Swinnerton-Dyer formula for $$E$$ if $$\operatorname{ord}_{s=1}L(E,s)\leq 1$$. They are also an ingredient in the proof of Kolyvagin’s conjecture and its cyclotomic variant in our joint work with Grossi [1]. 

Atmospheric rivers (ARs) bring concentrated rainfall and flooding to the western United States (US) and are hypothesized to have supported sustained hydroclimatic changes in the past. However, their ephemeral nature makes it challenging to document ARs in climate models and estimate their contribution to hydroclimate changes recorded by time-averaged paleoclimate archives. We present new climate model simulations of Heinrich Stadial 1 (HS1; 16,000 years before the present), an interval characterized by widespread wetness in the western US, that demonstrate increased AR frequency and winter precipitation sourced from the southeastern North Pacific. These changes are amplified with freshwater fluxes into the North Atlantic, indicating that North Atlantic cooling associated with weakened Atlantic Meridional Overturning Circulation (AMOC) is a key driver of HS1 climate in this region. As recent observations suggest potential weakening of AMOC, our identified connection between North Atlantic climate and northeast Pacific AR activity has implications for future western US hydroclimate. 

Atmospheric rivers (ARs) bring concentrated rainfall and flooding to the western United States (US) and are hypothesized to have supported sustained hydroclimatic changes in the past. However, their ephemeral nature makes it challenging to document ARs in climate models and estimate their contribution to hydroclimate changes recorded by time-averaged paleoclimate archives. We present new climate model simulations of Heinrich Stadial 1 (HS1; 16,000 years before the present), an interval characterized by widespread wetness in the western US, that demonstrate increased AR frequency and winter precipitation sourced from the southeastern North Pacific. These changes are amplified with freshwater fluxes into the North Atlantic, indicating that North Atlantic cooling associated with weakened Atlantic Meridional Overturning Circulation (AMOC) is a key driver of HS1 climate in this region. As recent observations suggest potential weakening of AMOC, our identified connection between North Atlantic climate and northeast Pacific AR activity has implications for future western US hydroclimate. 

We show that for certain non-CM elliptic curves E / Q E_{/\mathbb {Q}} such that 3 3 is an Eisenstein prime of good reduction, a positive proportion of the quadratic twists E ψ E_{\psi } of E E have Mordell–Weil rank one and the 3 3 -adic height pairing on E ψ ( Q ) E_{\psi }(\mathbb {Q}) is non-degenerate. We also show similar but weaker results for other Eisenstein primes. The method of proof also yields examples of middle codimensional algebraic cycles over number fields of arbitrarily large dimension (generalized Heegner cycles) that have non-zero p p -adic height. It is not known – though expected – that the archimedian height of these higher-codimensional cycles is non-zero. 

Résumé Soit $$E/{\mathbb {Q}}$$ E / Q une courbe elliptique à multiplication complexe et p un nombre premier de bonne réduction ordinaire pour E . Nous montrons que si $${\mathrm{corank}}_{{\mathbb {Z}}_p}{\mathrm{Sel}}_{p^\infty }(E/{\mathbb {Q}})=1$$ corank Z p Sel p ∞ ( E / Q ) = 1 , alors E a un point d’ordre infini. Le point de non-torsion provient d’un point de Heegner, et donc $${{{\mathrm{ord}}}}_{s=1}L(E,s)=1$$ ord s = 1 L ( E , s ) = 1 , ce qui donne une réciproque à un théorème de Gross–Zagier, Kolyvagin, et Rubin dans l’esprit de [49, 54]. Pour $$p>3$$ p > 3 , cela donne une nouvelle preuve du résultat principal de [12], que notre approche étend à tous les nombres premiers. L’approche se généralise aux courbes elliptiques à multiplication complexe sur les corps totalement réels [4]. 

Abstract We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of $${{\,\mathrm{GL}\,}}_3$$ GL 3 over imaginary quadratic fields, using the cohomology of Shimura varieties for $${\text {GU}}(2, 1)$$ GU ( 2 , 1 ) .