Algebraic Geometry

Get Equivariant Sheaves and Functors PDF

By Joseph Bernstein

ISBN-10: 3540580719

ISBN-13: 9783540580713

The equivariant derived type of sheaves is brought. All ordinary functors on sheaves are prolonged to the equivariant scenario. a few functions to the equivariant intersection cohomology are given. the idea should be precious to experts in illustration concept, algebraic geometry or topology.

Show description

Read or Download Equivariant Sheaves and Functors PDF

Similar algebraic geometry books

W. V. D. Hodge, D. Pedoe's Methods of algebraic geometry PDF

Within the 3rd quantity, the authors talk about algebraic forms on a flooring box with no attribute, and care for extra complicated geometrical tools, comparable to valuation concept.

Download PDF by Joseph Bernstein: Equivariant Sheaves and Functors

The equivariant derived class of sheaves is brought. All traditional functors on sheaves are prolonged to the equivariant state of affairs. a few purposes to the equivariant intersection cohomology are given. the speculation might be necessary to experts in illustration conception, algebraic geometry or topology.

Download PDF by David Mumford: Curves and Their Jacobians

Lecture 1, what's a curve and the way explicitly will we describe them? --Lecture 2, The moduli area of curves: definition, coordinatization, and a few houses. --Lecture three, How Jacobians and theta capabilities come up. --Lecture four, The Torelli theorem and the Schottky challenge

Additional info for Equivariant Sheaves and Functors

Example text

9. If Q(v1) = Q(v2))4 0 then Q(vl + V2) = 2Q(vi) + 2B(vi, V2) = 2B(vi, V1 + v2), implying Tv1+v2 (vl) = vl - (vl + v2) = -V2; likewise Tv1 _7J2 (vl) = V2. These facts help prove that the reflections generate the orthogonal group; cf. Exercises A12-A17. We are ready for the two major basic structure theorems of Witt. 10 (Witt Decomposition Theorem). Any quadratic space (V, Q) is an orthogonal sum of a totally isotropic space, a hyperbolic space, and an anisotropic space (any of which can be 0).

3'. 3(1), given submodules {Mi : i E I} of M, we define E Mi to be the set of all finite sums of elements from the Mi; this is the smallest submodule of M containing each Mi. 4. 1) f (ra) = r f (a) for all a, b in M and all r in R. Module homomorphisms are also called maps, and we favor this terminology, in order to avoid confusion with ring homomorphisms. 5. To check that f : M -* N is a map, one needs show that f (a + b) =f(a)+f(b) and f(ra) = r f (a) for all a, b in M and all r in R. Note. Recall that in linear algebra, the vector space V = F(') is often studied in terms of the ring of linear transformations from V to itself, which is identified with the matrix ring M,,(F).

3. The image of a homomorphism should be a structure. 4. The "kernel" of a homomorphism is of special interest to us, since it indicates what information is lost by applying the homomorphism. 5. We want to obtain Noether-type isomorphism theorems which relate the above concepts, via the notion of a factor structure. Rather than proceed formally with this program, we take several illustrative examples. Vector spaces and linear algebra 13 1. A monoid (M, 1, ) has the distinguished element 1 and the binary operation of multiplication, satisfying the sentences VaEM:1 dai E M : (ala2)a3 = al(a2a3) 2.

Download PDF sample

Equivariant Sheaves and Functors by Joseph Bernstein


by Jason
4.1

Rated 4.83 of 5 – based on 33 votes