Let $$E/{\mathbb {Q}}$$ be an elliptic curve and p odd prime where E has good reduction, assume that admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of over imaginary quadratic field in which splits, relate to characters by variation method Greenberg–Vatsal. As result our obtain proofs (under relatively mild hypotheses) Perrin-Riou’s Heegner point main conj...

Let N be a prime and let A be a quotient of J0(N) over Q associated to a newform such that the special L-value of A (at s = 1) is non-zero. Suppose that the algebraic part of the special L-value of A is divisible by an odd prime q such that q does not divide the numerator of N−1 12 . Then the Birch and Swinnerton-Dyer conjecture predicts that the q-adic valuations of the algebraic part of the s...

In this article, we study the Chow group of motive associated to a tempered global $L$-packet $\pi$ unitary groups even rank with respect CM extension, whose root number is $-1$. We show that, under some restrictions on ramification if central derivative $L'(1/2,\pi)$ nonvanishing, then $\pi$-nearly isotypic localization certain Shimura variety over its reflex field does not vanish. This proves...

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...