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Alternating variants of multiple poly-Bernoulli numbers and finite multiplezeta values in characteristic 0 and p  This paper consists of two parts: the characteristic 0 part and thecharacteristic p part. In characteristic 0 part, we introduce an alternatingextension of multiple poly-Bernoulli numbers of K. Imatomi, M. Kaneko and E.Takeda and obtain explicit presentations of the alternating finite multiplezeta values introduced by J. Zhao in term of the alternating extension ofmultiple poly-Bernoulli numbers. In characteristic p part, we introducepositive characteristic analogues of alternating finite multiple zeta valuesand express them as special values of finite Carlitz multiple polylogarithmsdefined by C.-Y. Chang and Y. Mishiba. We introduce alternating variants of R.Harada's multiple poly-Bernoulli-Carlitz numbers, which are analogues ofmultiple poly-Bernoulli numbers, to obtain explicit presentations of the finitealternating multiple zeta values. We show that any finite multiple zeta valuewith integer index is expressed as k-linear combination of FMZV's withall-positive indices.

Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p