Generic base change, Artin’s comparison theorem, and the decomposition theorem for complex Artin stacks

Enhanced Six Operations and Base Change Theorem for Artin Stacks

In this article, we develop a theory of Grothendieck’s six operations for derived categories in étale cohomology of Artin stacks. We prove several desired properties of the operations, including the base change theorem in derived categories. This extends all previous theories on this subject, including the recent one developed by Laszlo and Olsson, in which the operations are subject to more as...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

The Smooth Base Change Theorem

The Artin-schreier Theorem

The algebraic closure of R is C, which is a finite extension. Are there other fields which are not algebraically closed but have an algebraic closure which is a finite extension? Yes. An example is the field of real algebraic numbers. Since complex conjugation is a field automorphism fixing Q, and the real and imaginary parts of a complex number can be computed using field operations and comple...

Representation Theorem for Stacks

In this paper i is a natural number and x is a set. Let A be a set and let s1, s2 be finite sequences of elements of A. Then s1s2 is an element of A∗. Let A be a set, let i be a natural number, and let s be a finite sequence of elements of A. Then s i is an element of A∗. The following two propositions are true: (1) ∅ i = ∅. (2) Let D be a non empty set and s be a finite sequence of elements of...