Results 11 to 20 of about 66,173 (139)

Type classes for efficient exact real arithmetic in Coq [PDF]

, 2013
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer ...
Krebbers, Robbert, Spitters, Bas
core   +2 more sources

Complete intersections: Moduli, Torelli, and good reduction [PDF]

, 2016
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example,
A Hartmann, A Javanpeykar, A Javanpeykar, A Javanpeykar, A. Javanpeykar, AN Paršin, B Conrad, B Mazur, B Noohi, B Poonen, CAM Peters, CH Clemens, D Abramovich, D Edidin, D Rydh, D. Loughran, F Campana, G Faltings, H Flenner, J Carlson, J Rizov, J-P Serre, J-P Serre, J-X Cai, JWS Cassels, K Zuo, L Caporaso, M Demazure, M Rapoport, MC Olsson, O Benoist, O Debarre, O Gabber, P Deligne, R Jong de, S Mukai, Y André   +36 more
core   +2 more sources

Pathological behavior of arithmetic invariants of unipotent groups [PDF]

Algebra & Number Theory, 2019
We show that all of the nice behavior for Tamagawa numbers, Tate-Shafarevich sets, and other arithmetic invariants of pseudo-reductive groups over global function fields proved in \cite{rospred} fails in general for non-commutative unipotent groups.
Zev Rosengarten
semanticscholar   +1 more source

Two lectures on the arithmetic of K3 surfaces [PDF]

, 2013
In these lecture notes we review different aspects of the arithmetic of K3 surfaces. Topics include rational points, Picard number and Tate conjecture, zeta functions and modularity.Comment: 26 pages; v4: typos corrected, references ...
Schuett, Matthias
core   +1 more source

Notes on Number Theory

Mathematics
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-
Miroslav Stoenchev, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source

Analytic curves in algebraic varieties over number fields

, 2007
We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'
A Franchetta, B Dwork, C P Ramanujam, D G Cantor, D Harbater, D Mumford, D V Chudnovsky, D V Chudnovsky, E Kani, G Eisenstein, G Pólya, H Hironaka, H Hironaka, H Matsumura, H Randriambololona, J Fresnel, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-P. Serre, L Bădescu, L Moret-Bailly, L Moret-Bailly, M Raynaud, M van der Put, P Graftieaux, P Graftieaux, R Hartshorne, R Hartshorne, R Rumely, R S Rumely, S Bosch, S Bosch, S Bosch, V G Berkovich, W Gubler, Y Amice, Y André, Y Ihara, Yu. I. Manin, É Borel   +41 more
core   +5 more sources

Effectivity of Arakelov divisors and the theta divisor of a number field

, 1999
We introduce the notion of an effective Arakelov divisor for a number field and the arithmetical analogue of the dimension of the space of sections of a line bundle.
Schoof, René, van der Geer, Gerard
core   +1 more source

K-Rational D-Brane Crystals

, 2012
In this paper the problem of constructing spacetime from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of ...
Birch B. J., Birch B. J., Birch B. J., Cassels J. W. S., Cremona J. E., Kolyvagin V. A., Kolyvagin V. A., Kolyvagin V. A., Mordell L. J., ROLF SCHIMMRIGK, Tate J., Waldspurger J.-L., Wiles A.   +12 more
core   +1 more source

Strong minimality and the j-function [PDF]

, 2014
We show that the order three algebraic differential equation over ${\mathbb Q}$ satisfied by the analytic $j$-function defines a non-$\aleph_0$-categorical strongly minimal set with trivial forking geometry relative to the theory of differentially closed
J. Freitag, T. Scanlon
semanticscholar   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source