Results 1 to 10 of about 25,077 (188)

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., Calegari, Frank, Caraiani, Ana, Gee, Toby, Helm, David, Hung, Bao V. Le, Newton, James, Scholze, Peter, Taylor, Richard, Thorne, Jack A.   +9 more
core   +5 more sources

Euclidean Quadratic Forms and ADC Forms I [PDF]

, 2011
Motivated by classical results of Aubry, Davenport and Cassels, we define the notion of a Euclidean quadratic form over a normed integral domain and an ADC form over an integral domain.
Clark, Pete L.
core   +4 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, Hartmann, Julia, Krashen, Daniel   +2 more
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, Cohen, Darmon, Frank Thorne, Fröhlich, Greenberg, Henri Cohen, Nakagawa, Poitou, Scholz, Serre, Simon Rubinstein-Salzedo, Tate   +12 more
core   +5 more sources

Abelian Surfaces over totally real fields are Potentially Modular [PDF]

, 2018
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions.
Boxer, George, Calegari, Frank, Gee, Toby, Pilloni, Vincent   +3 more
core   +2 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

The Pythagoras number and the $u$-invariant of Laurent series fields in several variables

, 2015
We show that every sum of squares in the three-variable Laurent series field $\mathbb{R}((x,y,z))$ is a sum of 4 squares, as was conjectured in a paper of Choi, Dai, Lam and Reznick in the 1980's.
Hu, Yong
core   +1 more source

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  

Division Algebras and Quadratic Forms over Fraction Fields of Two-dimensional Henselian Domains

, 2014
Let $K$ be the fraction field of a 2-dimensional, henselian, excellent local domain with finite residue field $k$. When the characteristic of $k$ is not 2, we prove that every quadratic form of rank $\ge 9$ is isotropic over $K$ using methods of Parimala
Albert, Arason, Artin, Artin, Colliot-Thélène, Colliot-Thélène, Colliot-Thélène, Grothendieck, Grothendieck, Grothendieck, Grothendieck, Hoffmann, Lam, Lipman, Liu, Milne, Saito, Saltman, Saltman, Serre, Shafarevich, Yong Hu   +21 more
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