Structured Stable Homotopy Theory and the Descent Problem for
... KRepk [GF ] −→ KRepF [GF ] −→ V G (F ) and we are able to form derived completions for all these spectra attached to the homomorphism to the mod-l Eilenberg-MacLane spectrum which simply counts the dimension mod l of a vector space. We conjecture that a suitably equivariant version of this construct ...
... KRepk [GF ] −→ KRepF [GF ] −→ V G (F ) and we are able to form derived completions for all these spectra attached to the homomorphism to the mod-l Eilenberg-MacLane spectrum which simply counts the dimension mod l of a vector space. We conjecture that a suitably equivariant version of this construct ...
An Introduction to Algebra and Geometry via Matrix Groups
... complex numbers. We use these groups to motivate the definitions of groups, rings and fields, and to illustrate their properties. It is natural to generalize these matrix groups to general fields. In order to study these classical groups over arbitrary fields we discuss the theory of vector spaces o ...
... complex numbers. We use these groups to motivate the definitions of groups, rings and fields, and to illustrate their properties. It is natural to generalize these matrix groups to general fields. In order to study these classical groups over arbitrary fields we discuss the theory of vector spaces o ...
Matrix Groups
... complex numbers. We use these groups to motivate the definitions of groups, rings and fields, and to illustrate their properties. It is natural to generalize these matrix groups to general fields. In order to study these classical groups over arbitrary fields we discuss the theory of vector spaces o ...
... complex numbers. We use these groups to motivate the definitions of groups, rings and fields, and to illustrate their properties. It is natural to generalize these matrix groups to general fields. In order to study these classical groups over arbitrary fields we discuss the theory of vector spaces o ...
Real Algebraic Sets
... of a semialgebraic function y = f (t), restricted to a sufficiently small interval (0, ), is a branch of a real algebraic curve P (t, y) = 0 which can be parameterized by a Puiseux series y = σ(t) where σ is a root of the polynomial P ∈ R[t][y] in the field of fractions of real Puiseux series in t ...
... of a semialgebraic function y = f (t), restricted to a sufficiently small interval (0, ), is a branch of a real algebraic curve P (t, y) = 0 which can be parameterized by a Puiseux series y = σ(t) where σ is a root of the polynomial P ∈ R[t][y] in the field of fractions of real Puiseux series in t ...
Elements of Modern Algebra
... in their courses. Our basic goal in a single course has always been to reach the end of Section 5.3 “The Field of Quotients of an Integral Domain,” omitting the last two sections of Chapter 4 along the way. Other optional sections could also be omitted if class meetings are in short supply. The sect ...
... in their courses. Our basic goal in a single course has always been to reach the end of Section 5.3 “The Field of Quotients of an Integral Domain,” omitting the last two sections of Chapter 4 along the way. Other optional sections could also be omitted if class meetings are in short supply. The sect ...
An Introduction to Algebraic Number Theory, and the Class Number
... We describe various algebraic invariants of number fields, as well as their applications. These applications relate to prime ramification, the finiteness of the class number, cyclotomic extensions, and the unit theorem. Finally, we present an exposition of the class number formula, which generalizes ...
... We describe various algebraic invariants of number fields, as well as their applications. These applications relate to prime ramification, the finiteness of the class number, cyclotomic extensions, and the unit theorem. Finally, we present an exposition of the class number formula, which generalizes ...
Modular functions and modular forms
... From this, one sees that arithmetic facts about elliptic curves correspond to arithmetic facts about special values of modular functions and modular forms. For example, let 2 H be such that the elliptic curve E. / is defined by an equation with coefficients in an algebraic number field L. Then j. ...
... From this, one sees that arithmetic facts about elliptic curves correspond to arithmetic facts about special values of modular functions and modular forms. For example, let 2 H be such that the elliptic curve E. / is defined by an equation with coefficients in an algebraic number field L. Then j. ...
The structure of the classifying ring of formal groups with
... follows from Proposition 2.1.3 that the moduli stack of formal A-modules is a stack in the f pqc topology, has affine diagonal, and admits a formally smooth cover by an affine scheme, namely Spec LA , but this cover is only formally smooth and not smooth, since LA B is not finitely generated as an L ...
... follows from Proposition 2.1.3 that the moduli stack of formal A-modules is a stack in the f pqc topology, has affine diagonal, and admits a formally smooth cover by an affine scheme, namely Spec LA , but this cover is only formally smooth and not smooth, since LA B is not finitely generated as an L ...
Topological realizations of absolute Galois groups
... One can regard both of these theorems as instances of the general ‘tilting’ philosophy, [38], which relates objects of mixed characteristic with objects of equal characteristic, the latter of which have a more geometric flavour. An important feature of the tilting procedure is that it only works for ...
... One can regard both of these theorems as instances of the general ‘tilting’ philosophy, [38], which relates objects of mixed characteristic with objects of equal characteristic, the latter of which have a more geometric flavour. An important feature of the tilting procedure is that it only works for ...
