Tautological rings of spaces of pointed genus two curves of compact type

TY - JOUR

T1 - Tautological rings of spaces of pointed genus two curves of compact type

AU - Petersen, Dan Erik

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We prove that the tautological ring of , the moduli space of -pointed genus two curves of compact type, does not have Poincaré duality for any. This result is obtained via a more general study of the cohomology groups of. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of for any and considered both as -representation and as mixed Hodge structure/ -adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of is tautological for

AB - We prove that the tautological ring of , the moduli space of -pointed genus two curves of compact type, does not have Poincaré duality for any. This result is obtained via a more general study of the cohomology groups of. We explain how the cohomology can be decomposed into pieces corresponding to different local systems and how the tautological cohomology can be identified within this decomposition. Our results allow the computation of for any and considered both as -representation and as mixed Hodge structure/ -adic Galois representation considered up to semi-simplification. A consequence of our results is also that all even cohomology of is tautological for

KW - cohomology of moduli spaces

KW - Faber conjectures

KW - Gromov-Witten theory

KW - moduli of curves

KW - tautological ring

UR - http://www.scopus.com/inward/record.url?scp=84975108511&partnerID=8YFLogxK

U2 - 10.1112/s0010437x16007478

DO - 10.1112/s0010437x16007478

M3 - Journal article

AN - SCOPUS:84975108511

SN - 0010-437X

VL - 152

SP - 1398

EP - 1420

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 7

ER -