منابع مشابه
Homology and Cohomology of Stacks
Throughout this lecture, we let k denote an algebraically closed field, ` a prime number which is invertible in k. In the previous, we define the `-adic cohomology H∗(X; Λ), where X is a quasi-projective k-scheme and Λ ∈ {Z`,Q`,Z/`Z}. Our first goal in this lecture is to review the corresponding theory of `-adic homology. Definition 1. Let Λ be a commutative ring, and let ModΛ denote the∞-categ...
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One of the main obstacles for proving Riemann–Roch for algebraic stacks is the lack of cohomology and homology theories that are closer to the K-theory and G-theory of algebraic stacks than the traditional cohomology and homology theories for algebraic stacks. In this paper we study in detail a family of cohomology and homology theories which we call Bredon-style theories that are of this type ...
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The contact map of a protein fold is a graph that represents the patterns of contacts in the fold. It is known that the contact map can be decomposed into stacks and queues. RNA secondary structures are special stacks in which the degree of each vertex is at most one and each arc has length of at least two. Waterman and Smith derived a formula for the number of RNA secondary structures of lengt...
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The goal of this chapter is the construction of the presheaf of elliptic homology theories on the moduli stack of elliptic curves Mell . This sets the stage for many of the later chapters where the objective will be to turn this presheaf into to a sheaf of E∞-ring spectra (using obstruction theory). Even though we use the language of stacks, much of this chapter is closely related to the classi...
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Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H ], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly onX , in such a way that each stratum [S/H ] has a geometric quotient S/H . This leads to stratifications of moduli st...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1969-0250297-3