Add to ORKGWe relate the derivative of a p-adic Rankin-Selberg L-function to p-adic heights of the generalized Heegner cycles introduced by Bertolini, Darmon, and Prasanna. This generalizes the p-adic Gross-Zagier formulas of Perrin-Riou and Nekovar by allowing for Hecke characters of infinite order. As an application, we prove special cases of Perrin-Riou's p-adic Bloch-Kato conjecture. We also construct a Green's kernel in order to compute archimedean heights of generalized Heegner cycles. These computations will eventually lead to an archimedean version of our formula, generalizing the higher weight Gross-Zagier formula due to Zhang.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/b...
Darmon cycles are a higher weight analogue of Stark-Heegner points. They yield local cohomology clas...
We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian t...
We construct two-parameter analytic families of Galois cohomology classes interpolating the étale Ab...
We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a ...
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and ...
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and ...
In this thesis we study the so-called ``big Heegner points'' introduced and first studied by Ben How...
This article studies a distinguished collection of so-called generalized Heegner cycles in the produ...
International audienceWe prove a general formula for the $p$-adic heights of Heegner points on modul...
The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-...
Given a Hida family $\cal{F}$ of tame level $W$, for a quadratic imaginary field $K$ that satisfies ...
Let X be an Atkin-Lehner quotient of the modular curve X_0(N) whose Jacobian J_f is a simple quotien...
Let p be an odd prime. Given an imaginary quadratic field K = Q(sqrt(−D_K) where p splits with D_K >...
We study generalised Heegner cycles, originally introduced by Bertolini–Darmon–Prasanna for modular ...
Abstract. If E is an elliptic curve defined over a number field and p is a prime of good ordinary re...
Darmon cycles are a higher weight analogue of Stark-Heegner points. They yield local cohomology clas...
We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian t...
We construct two-parameter analytic families of Galois cohomology classes interpolating the étale Ab...
We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a ...
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and ...
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and ...
In this thesis we study the so-called ``big Heegner points'' introduced and first studied by Ben How...
This article studies a distinguished collection of so-called generalized Heegner cycles in the produ...
International audienceWe prove a general formula for the $p$-adic heights of Heegner points on modul...
The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-...
Given a Hida family $\cal{F}$ of tame level $W$, for a quadratic imaginary field $K$ that satisfies ...
Let X be an Atkin-Lehner quotient of the modular curve X_0(N) whose Jacobian J_f is a simple quotien...
Let p be an odd prime. Given an imaginary quadratic field K = Q(sqrt(−D_K) where p splits with D_K >...
We study generalised Heegner cycles, originally introduced by Bertolini–Darmon–Prasanna for modular ...
Abstract. If E is an elliptic curve defined over a number field and p is a prime of good ordinary re...
Darmon cycles are a higher weight analogue of Stark-Heegner points. They yield local cohomology clas...
We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian t...
We construct two-parameter analytic families of Galois cohomology classes interpolating the étale Ab...