The p -adic group ring ofSL2(pf)

Arbitrarily large Morita Frobenius numbers

“…and by our knowledge of the bases of A 1 and A 2 these elements are linearly independent modulo J 3 (A 1 ⊗ k A 2 ) and J 5 (A 1 ⊗ k A 2 ), respectively. Our claim follows using Proposition 5.4 (5).…”

“…By Proposition 5.4 (4) it follows that π(S ψ,φ ) = s ψ,φ ⊗ e 1 , and this element is not contained in J 2 (A 1 ⊗ k A 2 ). Hence S ψ,φ J 2 (B 0 ) by Proposition 5.4 (5). That is, the spaces on the right hand side are all one-dimensional.…”

Degenerating 0 in Triangulated Categories

“…(3) Note that assertion (2) implies assertion (3). Indeed, by the comments preceding Theorem 7, assertion (2) says that T 0 is the extension closure of {(S ⊕ S[t S ])[n] : S ∈ S and n ∈ Z}, for any choice of odd integers t S (S ∈ S).…”

“…Both concepts were highly successfully used in many places (cf. e.g., [3,4,6,7,[10][11][12]21]). Independently, Yoshino [20] gave a scheme theoretic definition for degenerations in the (triangulated) stable category of maximal Cohen-Macaulay modules, and he highlighted that in M ∆ N , one should assume that the induced endomorphism on Z should be nilpotent.…”

Degenerating $0$ in Triangulated Categories

“…Both concepts were highly successfully used in many places, cf e.g. [10,11,12,3,4,6,7,21]. Independently Yoshino [20] gave a scheme theoretic definition for degenerations in the (triangulated) stable category of maximal Cohen-Macaulay modules, and he highlighted that in M ≤ ∆ N one should assume that the induced endomorphism on Z should be nilpotent.…”