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The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties
(2017-05-13)
The orthogonal Shimura varieties are associated to special orthogonal groups over Q of signature (n, 2) at infinity. In this work we prove a version of Morel’s formula for the Frobenius-Hecke traces on the intersection ...
Nilpotence and Descent in Stable Homotopy Theory
(2017-04-18)
We study various applications of the ideas of descent and nilpotence to stable homotopy theory. In particular, we give a descent-theoretic calculation of the Picard group of topological modular forms and we prove a partial ...
The p-curvature conjecture and monodromy about simple closed loops
(2017-04-27)
The Grothendieck-Katz p-curvature curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its ...
Symmetric Powers and the Equivariant Dual Steenrod Algebra
(2017-05-09)
The structure of the Steenrod algebra of stable mod p cohomology operations and its dual A_* was worked out completely by Milnor - for every prime p, A_* is a graded-commutative Hopf algebra. However, much of this structure ...
Mod-P Isogeny Classes on Shimura Varieties With Parahoric Level Structure
(2017-05-11)
We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in \cite{KP}. We show that when the group is residually split, the points ...