Christopher Skinner
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View article: L-values and nonsplit extensions : a simplecase
L-values and nonsplit extensions : a simplecase Open
We explain a construction of explicit extensions -of rational Hodge structures and of p-adic Galois representations -in a simple context: the cohomology of ސ 1-{some points} relative to {some other points}.These extensions are naturally …
View article: Anti-cyclotomic Euler system of diagonal cycles
Anti-cyclotomic Euler system of diagonal cycles Open
We construct split anti-cyclotomic Euler systems for Galois representations attached to certain RACSDC automorphic representations on the group $\mathrm{GL}_n\times\mathrm{GL}_{n+1}$. As a result, we make progress towards certain rank 1 ca…
View article: Base change and Iwasawa Main Conjectures for ${\rm GL}_2$
Base change and Iwasawa Main Conjectures for ${\rm GL}_2$ Open
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…
View article: Higher Hida theory and p-adic L-functions for GSp4
Higher Hida theory and p-adic L-functions for GSp4 Open
We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent cohomology of Siegel threefolds in positive degrees. We ap…
View article: Syntomic regulators of Asai–Flach classes
Syntomic regulators of Asai–Flach classes Open
In this paper, we derive a formula for the $p$-adic syntomic regulators of Asai–Flach classes. These are cohomology classes forming an Euler system associated to a Hilbert modular form over a quadratic field, introduced in an earlier paper…
View article: A converse to a theorem of Gross, Zagier, and Kolyvagin
A converse to a theorem of Gross, Zagier, and Kolyvagin Open
Let $E$ be a semistable elliptic curve over $\mathbb{Q}$. We prove that if $E$ has non-split multiplicative reduction at at least one odd prime or split multiplicative reduction at at least two odd primes and if the rank of $E(\mathbb{Q})$…
View article: Statistics of K-groups modulo p for the ring ofintegers of a varying quadratic number field
Statistics of K-groups modulo p for the ring ofintegers of a varying quadratic number field Open
For each odd prime [math] , we conjecture the distribution of the [math] -torsion subgroup of [math] as [math] ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the [math] -torsio…
View article: On the Iwasawa main conjectures for modular forms at non-ordinary primes
On the Iwasawa main conjectures for modular forms at non-ordinary primes Open
In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on the study of the two-variable analogues of these conjectures …
View article: A Homological Definition for the Tate--Shafarevich Group of a Pell Conic
A Homological Definition for the Tate--Shafarevich Group of a Pell Conic Open
Franz Lemmermeyer's previous work laid the framework for a description of the arithmetic of Pell conics, which is analogous to that of elliptic curves. He describes a group law on conics and conjectures the existence of an analogous Tate--…
View article: Ad Honorem Sir Andrew J. Wiles
Ad Honorem Sir Andrew J. Wiles Open
Prize in a ceremony held in the Aula of the University of Oslo in Oslo, Norway.Wiles, who received the prize from H.R.H. Crown Prince Haakon at the award ceremony, was the fourteenth recipient of the 6 million NOK (about 750,000 USD) prize…
View article: p-adic L-functions for unitary groups, part II: zeta-integral calculations
p-adic L-functions for unitary groups, part II: zeta-integral calculations Open
This paper completes key steps toward a construction of $p$-adic $L$-functions for unitary groups. More precisely, in 2006, the last three authors proposed an approach to constructing $p$-adic $L$-functions for unitary groups. Building on …