Results 11 to 20 of about 156,086 (209)

The elementary obstruction and homogeneous spaces [PDF]

, 2008
Let $k$ be a field of characteristic zero and ${\bar k}$ an algebraic closure of $k$. For a geometrically integral variety $X$ over $k$, we write ${\bar k}(X)$ for the function field of ${\bar X}=X\times_k{\bar k}$.
Borovoi, M., Colliot-Thélène, J-L., Skorobogatov, A. N.   +2 more
core   +1 more source

The Bogomolov conjecture for totally degenerate abelian varieties [PDF]

, 2006
We prove the Bogomolov conjecture for an abelian variety A over a function field which is totally degenerate at a place v. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry.
Gubler, Walter
core   +1 more source

Explicit root numbers of abelian varieties [PDF]

, 2019
The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the functional equation of its $L$-function, known as the global root number ...
Bisatt, Matthew
core   +3 more sources

Using Elimination Theory to construct Rigid Matrices [PDF]

, 2013
The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r.
Abhinav Kumar, B. Codenotti, J. Friedman, J. Heintz, J. KollÁr, M. N. Jayalal Sarma, S.V. Lokam, S.V. Lokam, S.V. Lokam, Satyanarayana V. Lokam, Vijay M. Patankar, W.D. Brownawell   +11 more
core   +2 more sources

J-invariant of linear algebraic groups [PDF]

, 2007
Let G be a linear algebraic group over a field F and X be a projective homogeneous G-variety such that G splits over the function field of X. In the present paper we introduce an invariant of G called J-invariant which characterizes the motivic behaviour
Petrov, Victor, Semenov, Nikita, Zainoulline, Kirill   +2 more
core   +4 more sources

Survey on the geometric Bogomolov conjecture [PDF]

, 2017
This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory over function
Yamaki, Kazuhiko
core   +3 more sources

Flexible varieties and automorphism groups [PDF]

, 2012
Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., the subgroup of the full automorphism group Aut (X) generated by all one-parameter unipotent subgroups. We show that if SAut (X)
Arzhantsev, I., Flenner, H., Kaliman, S., Kutzschebauch, F., Zaidenberg, M.   +4 more
core   +2 more sources

Growth of generating sets for direct powers of classical algebraic structures [PDF]

, 2010
For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A.
Quick, Martyn, Ruskuc, Nik
core   +1 more source

On Ihara's lemma for Hilbert Modular Varieties

, 2008
Let \rho be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that \rho has large image and admits a low weight crystalline modular deformation we show that any low weight crystalline deformation
Darmon, Dimitrov, Fontaine, Fontaine, Mladen Dimitrov, Mokrane, Rajaei, Ramakrishna, Skinner, Taylor, Taylor   +10 more
core   +1 more source

The wave front set of the Fourier transform of algebraic measures [PDF]

, 2014
We study the Fourier transform of the absolute value of a polynomial on a finite-dimensional vector space over a local field of characteristic 0. We prove that this transform is smooth on an open dense set.
Aizenbud, Avraham, Drinfeld, Vladimir
core   +1 more source