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Therefore Corollary 2.3 tells us that only the dihedral quandle is useful in Alexander quandles of prime order for the study of quandle cocycle invariants of 1-knots and 2-knots..

We know that the function u ˜ i is p(·)-quasicontinuous; notice here that [21], Theorem 2, improves [15], Theorem 4.6 by showing that our standard assumptions are sufficient for

“Breuil-M´ezard conjecture and modularity lifting for potentially semistable deformations after

Finally, as a corollary Theorem 4.7 and Proposition 4.9, we obtain the relative birational version of the Grothendieck Conjecture for smooth curves over subfields of finitely

We also obtain some injectivity results (cf. Propositions 2.13 and 2.16) on homomorphisms between the fil- tered absolute Galois groups of GMLF’s (by using the theory of fields of

Q is contained in the graph of a

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