Results 1 to 10 of about 25,152 (191)
Potential automorphy over CM fields [PDF]
, 2022 Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition.
Allen, Patrick B. +9 more
core +5 more sources
Heights and quadratic forms: on Cassels' theorem and its generalizations [PDF]
, 2012 In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally ...
Fukshansky, Lenny
core +2 more sources
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains [PDF]
, 2012 Let $R$ be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let $L$ and $k$ be respectively its fraction field and residue field.
Hu, Yong
core +2 more sources
Quadratic forms and linear algebraic groups [PDF]
, 2009 Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties ...
Harbater, David +2 more
core +1 more source
Rings and ideals parametrized by binary n-ic forms [PDF]
, 2010 The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic forms, and found that ideal classes of quadratic rings ...
Wood, Melanie Matchett
core +1 more source
Identities for field extensions generalizing the Ohno-Nakagawa relations [PDF]
, 2015 In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences
Cohen +12 more
core +5 more sources
A cohomological Hasse principle over two-dimensional local rings
, 2016 Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$.
Hu, Yong
core +1 more source
Descent and forms of tensor categories [PDF]
, 2011 We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of forms.
Etingof, Pavel, Gelaki, Shlomo
core +3 more sources
Octonion algebras over rings are not determined by their norms [PDF]
, 2012 Answering a question of H. Petersson, we provide a class of examples of pair of octonion algebras over a ring having isometric norms.Comment: 8 ...
Gille, Philippe
core +3 more sources
Remarks on the Milnor conjecture over schemes [PDF]
, 2011 The Milnor conjecture has been a driving force in the theory of quadratic forms over fields, guiding the development of the theory of cohomological invariants, ushering in the theory of motivic cohomology, and touching on questions ranging from sums of ...
Auel, Asher
core