Results 21 to 30 of about 6,169 (67)
Arithmetic Satake compactifications and algebraic Drinfeld modular forms
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
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Carlitz operators and higher polylogarithm identities
Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.Abstract We study a higher dimension generalization of Carlitz's polynomials, first introduced by Papanikolas, and compute an ∞$\infty$‐adic limit of a sequence of normalizations, relating it to the exponential function of an Anderson module that we completely describe.
F. Pellarin
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Sparsity of stable primes for dynamical sequences
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 203-217, January 2025.Abstract We show that a dynamical sequence (fn)n∈N$(f_n)_{n\in \mathbb {N}}$ of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and, in particular, virtually prosolvable dynamical Galois group. Together with existing heuristics, our results suggest, moreover, that a polynomial f$
Joachim König
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Rational points on 3‐folds with nef anti‐canonical class over finite fields
Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.Abstract We prove that a geometrically integral smooth projective 3‐fold X$X$ with nef anti‐canonical class and negative Kodaira dimension over a finite field Fq$\mathbb {F}_q$ of characteristic p>5$p>5$ and cardinality q=pe>19$q=p^e > 19$ has a rational point.
Fabio Bernasconi, Stefano Filipazzi
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Dynamical diophantine approximation exponents in characteristic p$p$
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3801-3818, December 2024.Abstract Let ϕ(z)$\phi (z)$ be a non‐isotrivial rational function in one‐variable with coefficients in F¯p(t)$\overline{\mathbb {F}}_p(t)$ and assume that γ∈P1(F¯p(t))$\gamma \in \mathbb {P}^1(\overline{\mathbb {F}}_p(t))$ is not a post‐critical point for ϕ$\phi$. Then we prove that the diophantine approximation exponent of elements of ϕ−m(γ)$\phi ^{-m}
Wade Hindes
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On Weil–Stark elements, I: Construction and general properties
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We construct a canonical family of elements in the reduced exterior powers of unit groups of global fields and investigate their detailed arithmetic properties. We then show that these elements specialise to recover the classical theory of cyclotomic elements in real abelian fields and also have connections to the theory of non‐commutative ...
David Burns +2 more
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Universal quadratic forms and Northcott property of infinite number fields
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals Q$\mathbb {Q}$, then the set of totally positive integers in the extension does not have the Northcott property. In particular, this implies that no universal form exists over the compositum of all totally real Galois ...
Nicolas Daans +2 more
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Galois invariants of finite abelian descent and Brauer sets
Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3240-3256, October 2024.Abstract For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer–Manin obstructions. Given a Galois extension of the ground field, one can consider similar sets over the extension and take Galois invariants.
Brendan Creutz +2 more
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On tame ramification and centers of F$F$‐purity
Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract We introduce a notion of tame ramification for general finite covers. When specialized to the separable case, it extends to higher dimensions the classical notion of tame ramification for Dedekind domains and curves and sits nicely in between other notions of tame ramification in arithmetic geometry. However, when applied to the Frobenius map,
Javier Carvajal‐Rojas, Anne Fayolle
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Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces. [PDF]
Entropy (Basel), 2023 Derr R, Williamson RC.
europepmc +1 more source