✦ LIBER ✦

Homology of hyperelliptic mapping class groups for surfaces

✍ Scribed by Nariya Kawazumi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 761 KB
Volume: 76
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(96)00105-8

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✦ Synopsis

The cohomology of the hyperelliptic mapping class group of genus g with coefficients in any field has been determined by Boedigheimer-Cohen-Peim.

We give an alternative, more geometric and elementary way to compute it when the characteristic of the field is greater than g.

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Let q be an odd prime, e a non-square in the finite field F q with q elements, p(T) an irreducible polynomial in F q [T] and A the affine coordinate ring of the hyperelliptic curve y 2 =ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4