For $g\geq2$, $j=1,\dots,g$ and $n\geq g+j$ we exhibit infinitely many new rigid extremal effective codimension $j$ cycles in $\overline{\mathcal{M}}_{g,n}$ from the strata of quadratic differentials projections these under forgetful morphisms show same holds for $k$-differentials with $k\geq 3$ if are irreducible. We compute class divisors case which contain first known examples on negative $\...

Let k be a perfect field of characteristic p>0, let A_d the coordinate ring axes in affine d-space over k, and I_d ideal defining origin. We evaluate relative K-groups K_q(A_d,I_d) terms p-typical Witt vectors k. When d=2 result is due to Hesselholt, for K_2 it Dennis Krusemeyer. also compute groups case where an ind-smooth algebra rationals, being expressed algebraic de Rham forms. zero this c...