Intersection theory on algebraic stacks and on their moduli spaces

Vistoli, Angelo

doi:10.1007/bf01388892

Cited by 395 publications

(392 citation statements)

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“…Since ψ q · D = 0, the first term of (24) is given by where Ξ (1) and Ξ (2) are defined in (19) and (20), respectively. As a result of Theorem 2 and the definition of tautological classes, we get new elements in the tautological ring of M g,P .…”

Section: The Chern Character Of M Gpmentioning

confidence: 99%

Chern Classes of the Moduli Stack of Curves

Bini

2005

Mathematical Research Letters

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Section: The Chern Character Of M Gpmentioning

confidence: 99%

Chern Classes of the Moduli Stack of Curves

Bini

2005

Mathematical Research Letters

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“…The use of these ideas has expanded to the point where there is now a whole cottage industry on stacks, and they are supposed to be part of our basic tool kit. The standard book reference on this subject is [27] and a concise introduction to the algebraic geometry point of view is in the appendix to [41]. A relative recent introductory paper also exists; see [16].…”

Section: An Extremely Short Introduction To Stacksmentioning

confidence: 99%

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

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In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem.While some of what I say is quite general, the ring spectra I have in mind will arise from the chromatic point of view, which uses the geometry of formal groups to organize stable homotopy theory. Thus, a subsidiary aim here is to reemphasize this connection between algebraic geometry and homotopy theory.

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“…This implies that ω V is G-equivariantly trivial, so that we can apply the above result. Note that if X is a normal quasi-projective variety with quotient singularities, then there is always a smooth separated Deligne-Mumford stack associated to it as in the above statement (see proposition 2.8 of [21]). The non-trivial hypothesis (which can not be removed) is that the dualizing bundle of the Deligne-Mumford stack associated to X is the pull back of the dualizing bundle on X .…”

Section: Corollary 3013 Let V Be a Finite Dimensional Vector Space mentioning

confidence: 99%