Non-abelian Local Invariant Cycles

2004/11/23 by Yen-lung Tsai, Tsai, Yen-lung, Eugene Z. Xia +1
Mathematics · #14D05 #20F34 #55N2 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D05 #msc:20F34 #msc:55N2

paper · pdf · doi:10.48550/arxiv.math/0411504

4 pages

arxiv created 2004/11/23 · arxiv updated 2009/12/01

Abstract

Let f be a degeneration of Kahler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodromy action, rises from a global cohomology class. Instead of the classical cohomology, one may consider the non-abelian cohomology. This note demonstrates that the analogous non-abelian version of the local invariant cycle theorem does not hold if the first non-abelian cohomology is the moduli space (universal categorical quotient) of the representations of the fundamental group.

Related

• The local monodromy as a generalized algebraic correspondence
• Abelian and non-abelian cohomology
• Local and global invariant cycle theorems for Hodge modules
• On the p-adic local invariant cycle theorem
• On p-adic invariant cycles theorem