We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...

Let K be a real quadratic number field. Let p be a prime which is inert in K. We denote the completion of K at the place p by Kp. Let f > 1 be a positive integer coprime to p. In this thesis we give a p-adic construction of special elements u(r, τ) ∈ K× p for special pairs (r, τ) ∈ (Z/fZ)× × Hp where Hp = P(Cp)\P(Qp) is the so called p-adic upper half plane. These pairs (r, τ) can be thought of...

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...

We describe an algorithm for solving systems of univariate p-adic constraints. In analogy with univariate real constraints, we formalize univariate p-adic constraints as univariate polynomial equations and order comparisons between p-adic values of univariate polynomials. Systems of constraints are arbitrary boolean combinations of such constraints. Our method combines techniques of Presburger ...

For varieties over a perfect field of characteristic p, étale cohomology with Q`coefficients is a Weil cohomology theory only when ` 6= p; the corresponding role for ` = p is played by Berthelot’s rigid cohomology. In that theory, the coefficient objects analogous to lisse `-adic sheaves are the overconvergent F -isocrystals. This expository article is a brief user’s guide for these objects, in...

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic absolute value in Cp is normalized in such a way that |p|p 1/p see 1–17 . Fo...

In this paper we considered a moving from classical logic and Kolmogorov’s probability theory to non-classical p-adic valued logic and p-adic valued probability theory. Namely, we defined p-adic valued logic and further we constructed probability space for some ideals on truth values of p-adic valued logic. We proposed also p-adic valued inductive logic. Such a logic was considered for the firs...

Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...