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Parametric Expansions of an Algebraic Variety Near Its Singularities II
AxiomsThe paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities.
Alexander D. Bruno, A. A. Azimov
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Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties [PDF]
Mathematical Research Letters, 2021 This is a companion paper to our previous work, where we proved the finiteness of the Tate-Shafarevich group for an arbitrary torus $T$ over a finitely generated field $K$ with respect to any divisorial set $V$ of places of $K$.
A. Rapinchuk, I. Rapinchuk
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Operator index of a nonsingular algebraic curve
Turkish Journal of Mathematics, 2023 : The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated.
A. Dosi
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Arab Journal of Basic and Applied Sciences, 2021 Numerical solutions to differential and integral equations have been a very active field of research. The necessary tools to solving differential equations can add much fuel for acceleration of scientific development.
Hajra Zeb +3 more
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Geometric rank of tensors and subrank of matrix multiplication
Discrete Analysis, 2023 Geometric rank of tensors and subrank of matrix multiplication, Discrete Analysis 2023:1, 25 pp. The rank of a matrix is a parameter of obvious importance, so it is natural to wonder what the right definition is for the rank of a higher-dimensional ...
Swastik Kopparty +2 more
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Structure vs Randomness for Bilinear Maps
Discrete Analysis, 2022 Structure vs randomness for bilinear maps, Discrete Analysis 2022:12, 21 pp. A _tensor_ can be thought of as a higher-dimensional analogue of a matrix (where a matrix is 2-dimensional).
Guy Moshkovitz, Alex Cohen
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Equidistribution of dynamically small subvarieties over the function field of a curve [PDF]
, 2008 For a projective variety X defined over a field K, there is a special class of self-morphisms of X called algebraic dynamical systems. In this paper we take K to be the function field of a smooth curve and prove that at each place of K, subvarieties of X
X. Faber
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Algebraic dynamics of skew-linear self-maps [PDF]
, 2018 Let $X$ be a variety defined over an algebraically closed field $k$ of characteristic $0$, let $N\in\mathbb{N}$, let $g:X\dashrightarrow X$ be a dominant rational self-map, and let $A:\mathbb{A}^N\to \mathbb{A}^N$ be a linear transformation defined over $
D. Ghioca, Junyi Xie
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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. +2 more
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Elliptic curves and Hilbert’s tenth problem for algebraic function fields over real and p-adic fields [PDF]
, 2004 Let k be a field of characteristic zero, V a smooth, positive-dimensional, quasiprojective variety over k, and Q a nonempty divisor on V. Let K be the function field of V, and A ⊂ K the semilocal ring of Q. We prove the Diophantine undecidability of:
L. Moret-Bailly
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