Okaaaay... which position?
Alekhine-Hofmeister, Petrograd 1917
The OP has had one too many Hofmeisters, I'm guessing. 
1 a7 mate (hm...)
Indeed. Did Alekhine really miss that?
I very much doubt that a master of tactics like Alekhine would miss something so simple. I've made a search of the net and am unable to find the whole game, indeed there seems to be differing positions given in various articles. One article even claims this game was played at odds but does not say which odds. If anyone has a link to the game, please post here.
p.s. Kasparov gives an analysis in "My Great Predecessors" (Vol 1, item 115).
This section in the Combinations of Alekhine Course states that dxc7 loses to Rxc7, but after Bxa7 Kxa7 that line ends with a Mate in 2. Bxc7+ does prevent the mate, but black is still losing. While the move given in the module is the best move, the comments for dxc7 are incorrect