We discuss p-adic unipotent Albanese maps for curves of positive genus, extending the theory of p-adic multiple polylogarithms. This construction is then used to relate linear Diophantine conjectures of ‘Birch and Swinnerton-Dyer type’ to non-linear theorems of Faltings-Siegel type. In a letter to Faltings [14] dated June, 1983, Grothendieck proposed several striking conjectural connections bet...

Let π1,…,πk be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product π1×⋯×πk has a unique quotient whose Langlands parameter is sum parameters all factors (cyclicity property), assuming same property holds for each products πi×πj (i<j), and but at most two πi×πi remains (square-irreducibility property). Our technique applies recently d...

We study the p-adic algebraic groups G from definable topological-dynamical point of view. consider case where M is an arbitrary closed field and group over Qp admitting Iwasawa decompostion G=KB, K open definably compact Qp, B a Borel subgroup Qp. Our main result explicit description minimal subflow Ellis universal G(M)-flow SG(Mext). prove that SG(Mext) isomorphic to SB(Mext), which B/B0. As ...

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu’s construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu’s construction, Fourier transforms of orbital integr...

Let F be a non-Archimedean local field. LetG stand for the F -points of a connected reductive algebraic group defined over F . We will refer to G as a p-adic group, with the understanding that the base field F is fixed once and for all. We let R(G) denote the category of smooth complex representations of G. It is well known [1] that this is an abelian category and has enough projectives and hen...

We calculate extensions between certain irreducible admissible representations of p-adic groups. To Hiroshi Saito, in memoriam

p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief re...