Ratios of congruent numbers
Ray class fields of global function fields with many rational places
Rechnen in endlichen Körpern (Beispiele elementarer Zahlentheorie).
Reciprocity laws on curves
Recognition of simple singularities in positive characteristic.
Reduction and lifting of special metacyclic covers
Reduction and specialization of polynomials
We show explicit forms of the Bertini-Noether reduction theorem and of the Hilbert irreducibility theorem. Our approach recasts in a polynomial context the geometric Grothendieck good reduction criterion and the congruence approach to HIT for covers of the line. A notion of “bad primes” of a polynomial P ∈ ℚ[T,Y] irreducible over ℚ̅ is introduced, which plays a central and unifying role. For such a polynomial P, we deduce a new bound for the least integer t₀ ≥ 0 such that P(t₀,Y) is irreducible...
Reduction of the Manin map modulo p.
Reed-Muller codes and supersingular curves. I
Reelle algebraische Funktionen mit vorgegebenen Null- und Polstellen.
Refined theorems of the Birch and Swinnerton-Dyer type
In this paper, we generalize the context of the Mazur-Tate conjecture and sharpen, in a certain way, the statement of the conjecture. Our main result will be to establish the truth of a part of these new sharpened conjectures, provided that one assume the truth of the classical Birch and Swinnerton-Dyer conjectures. This is particularly striking in the function field case, where these results can be viewed as being a refinement of the earlier work of Tate and Milne.
Reflections on Fermat's Last Theorem.
Reflective functions on p-adic fields
Régulateurs syntomiques et valeurs de fonctions L p-adiques II.
Régulateurs syntomiques et valeurs de fonctions Lp-adiques I.
Relations between jacobians of modular curves of level
We derive a relation between induced representations on the group which implies a relation between the jacobians of certain modular curves of level . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of .
Relations monomiales entre périodes p-adiques.
Relative ampleness in rigid geometry
We develop a rigid-analytic theory of relative ampleness for line bundles and record some applications to faithfully flat descent for morphisms and proper geometric objects. The basic definition is fibral, but pointwise arguments from the algebraic and complex-analytic cases do not apply, so we use cohomological properties of formal schemes over completions of local rings on rigid spaces. An analytic notion of quasi-coherence is introduced so that we can recover a proper object from sections of...
Relèvement de schémas et algèbres de Monsky-Washnitzer : théorèmes d’équivalence et de pleine fidélité
Report on Igusa's local zeta function