Related papers: An equivariant $p$-adic Artin conjecture

By means of the theory of strongly semistable sheaves and of the theory of the Greenberg transform, we generalize to higher dimensions a result on the sparsity of p-divisible unramified liftings which played a crucial role in Raynaud's…

We conjecture that a $p$-algebra over a complete discrete valued field $K$ contains a totally ramified purely inseparable subfield if and only if it contains a totally ramified cyclic maximal subfield. We prove the conjecture in several…

This article is devoted to the elliptic Stark conjecture formulated by Darmon, Lauder and Rotger [DLR], which proposes a formula for the transcendental part of a $p$-adic avatar of the leading term at $s=1$ of the Hasse-Weil-Artin…

This article is an expanded version of the talk given by the first author at the conference "Exponential sums over finite fields and applications" (ETH, Z\"urich, November, 2010). We state some conjectures on archimedian and $p$-adic…

We present a comprehensive study of the geometry of Hilbert $p$-adic eigenvarieties at classical parallel weight one intersection points of their cuspidal and Eisenstein loci. For instance, we determine all such points at which the weight…

We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the…

We establish an effective Bertini-type theorem for hypersurfaces $X_f \colon f = 0$ defined over a finite field $k$ for which $f$ has no linear factors over the algebraic closure $\overline{k}$. Given a line $L$ defined over $k$ and a…

Let L/k be a finite Galois extension of number fields with Galois group G. For every odd prime p satisfying certain mild technical hypotheses, we use values of Artin L-functions to construct an element in the centre of the group ring…

We describe Greenberg's pseudo-null conjecture, and prove a result describing conditions under which the pseudo-null conjecture for a number field $K$ implies the conjecture for finite extensions of $K$. We then apply the result to the…

We give a new and elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the…

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_2)$ and an ordinary $R = \mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the…

Let $\mathbb{K}$ be an imaginary quadratic field such that $2$ splits into two primes $\mathfrak{p}$ and $\bar{\mathfrak{p}}$. Let $\mathbb{K}_{\infty}$ be the unique $\mathbb{Z}_2$-extension of $\mathbb{K}$ unramified outside…

In this paper, we prove the generalised Andr\'e-Pink-Zannier conjecture (an important case of the Zilber-Pink conjecture) for all Shimura varieties of abelian type. Questions of this type were first asked by Y. Andr\'e in 1989. We actually…

We construct a $p$-adic $L$-function for $P$-ordinary Hida families of cuspidal automorphic representations on a unitary group $G$. The main new idea of our work is to incorporate the theory of Schneider-Zink types for the Levi quotient of…

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is…

We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if W is such a variety, then every piecewise polynomial function on W can be written as…

We study the local epsilon constant conjecture as formulated by Breuning. This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected…

The main conjectures of Iwasawa theory provide the only general method known at present for studying the mysterious relationship between purely arithmetic problems and the special values of complex L-functions, typified by the conjecture of…

In this paper we give a short, elementary proof of the following too extreme cases of the Leopoldt conjecture: the case when $\K/\Q$ is a solvable extension and the case when it is a totally real extension in which $p$ splits completely.…

Let $p\geq 5$ be a prime, and $\mathfrak{p}$ a prime of $\bar{\mathbb{Q}}$ above $p$. Let $g_1$ and $g_2$ be $\mathfrak{p}$-ordinary, $\mathfrak{p}$-distinguished and $p$-stabilized cuspidal newforms of nebentype characters $\epsilon_1,…