Related papers: P-adic heights and p-adic Hodge theory

We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…

Let $\mathfrak q$ be a Lie algebra over a field $\mathbb K$ and $p,\tilde p\in\mathbb K[t]$ two different normalised polynomials of degree at least 2. As vector spaces both quotient Lie algebras $\mathfrak q[t]/(p)$ and $\mathfrak…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…

Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of…

This work is devoted to the study of integral $p$-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of $p$-adic Hodge theory with the \'etale…

For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized…

The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The…

We give a direct proof that the Mazur-Tate and Coleman-Gross heights on elliptic curves coincide. The main ingredient is to extend the Coleman-Gross height to the case of divisors with non-disjoint support and, doing some $p$-adic analysis,…

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology. We use this to compute the homotopy cofiber of a transfer map K(L/p) --> K(L_p), which we interpret as the algebraic…

For a polynomial $f(x)$ in $(\mathbb{Z}_p\cap \mathbb{Q})[x]$ of degree $d>2$ let $L(f \bmod p;T)$ be the $L$-function of the exponential sum of $f \bmod p$. Let $\mathrm{NP}(f \bmod p)$ denote the Newton polygon of $L(f \bmod p;T)$. Let…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

We wish to use graded structures [KrVu87], [Vu01] on dffierential operators and quasimodular forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corresponding…

Bertolini-Darmon and Mok proved a formula of the second derivative of the two-variable $p$-adic $L$-function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…

We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…

We introduce a systematic theory of Weil bundles over \( p \)-adic analytic manifolds, forging new connections between differential calculus over non-archimedean fields and arithmetic geometry. By developing a framework for infinitesimal…

In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these…

This article presents an approach to the algebraic functional equation for Selmer complexes, which in turn have applications in the Iwasawa theoretic study of Rankin-Selberg products of the Hida and Coleman families. Our treatment…

We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.

We prove an analog of Schmid's $\text{\rm SL}_2$-orbit theorem for a class of variations of mixed Hodge structure which includes logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as consequence…